diff --git a/src/qldpc/circuits/transversal.py b/src/qldpc/circuits/transversal.py
index 09c26cb8d..1b535e580 100644
--- a/src/qldpc/circuits/transversal.py
+++ b/src/qldpc/circuits/transversal.py
@@ -96,6 +96,9 @@ def get_transversal_automorphism_group(
 
     Uses the methods of https://arxiv.org/abs/2409.18175.
     """
+    if not local_gates:
+        return abstract.Group(abstract.GroupMember(range(len(code))))
+
     local_gates = _validate_local_gates(local_gates)
     allow_swaps = "SWAP" in local_gates
     local_gates.discard("SWAP")
@@ -122,10 +125,31 @@ def get_transversal_automorphism_group(
         # we are looking for transversal gates involving only two-qubit SWAPs
         matrix: npt.NDArray[np.int_] = parity_checks
         _code = codes.QuditCode(matrix).maybe_to_css()
-        if isinstance(_code, codes.CSSCode) and np.array_equal(
-            (canonicalized_code := _code.canonicalized).matrix_x, canonicalized_code.matrix_z
-        ):
-            matrix = canonicalized_code.matrix_x
+        if isinstance(_code, codes.CSSCode):
+            canonicalized_code = _code.canonicalized
+            if np.array_equal(canonicalized_code.matrix_x, canonicalized_code.matrix_z):
+                # Self-dual CSS: column permutations preserving H_x automatically preserve H_z
+                matrix = canonicalized_code.matrix_x
+            else:
+                # Non-self-dual CSS: the joint parity-check matrix has block-diagonal support, so
+                # its column-permutation automorphism group factors as Aut(H_x) x Aut(H_z) on
+                # disjoint column sets.  SWAPs act diagonally on X- and Z-columns, so the SWAP
+                # transversal group is Aut(H_x) ∩ Aut(H_z). Recurse on fake self-dual codes built
+                # from H_x and H_z so the self-dual branch above handles each half, then intersect.
+                fake_code_x = codes.CSSCode(
+                    canonicalized_code.matrix_x, canonicalized_code.matrix_x
+                )
+                fake_code_z = codes.CSSCode(
+                    canonicalized_code.matrix_z, canonicalized_code.matrix_z
+                )
+                group_x = get_transversal_automorphism_group(
+                    fake_code_x, ["SWAP"], deform_code=False, with_magma=with_magma
+                )
+                group_z = get_transversal_automorphism_group(
+                    fake_code_z, ["SWAP"], deform_code=False, with_magma=with_magma
+                )
+                generators = _sympy_group_intersection_generators(group_x, group_z)
+                return abstract.Group(*map(abstract.GroupMember, generators))
 
     else:
         # we are looking for transversal gates involving two-qubit SWAPs and single-qubit Cliffords
diff --git a/src/qldpc/circuits/transversal_test.py b/src/qldpc/circuits/transversal_test.py
index 005afb490..fe9528c62 100644
--- a/src/qldpc/circuits/transversal_test.py
+++ b/src/qldpc/circuits/transversal_test.py
@@ -28,17 +28,22 @@
 
 def test_transversal_ops() -> None:
     """Construct SWAP-transversal logical Cliffords of a code."""
-    code = codes.ToricCode(2)
+    code: codes.CSSCode
 
-    for local_gates in [
-        ["SWAP"],
-        ["SWAP", "H"],
-        ["SWAP", "S"],
-        ["SWAP", "SQRT_X"],
-        ["SWAP", "H", "S"],
-    ]:
-        transversal_ops = circuits.get_transversal_ops(code, local_gates)
-        assert len(transversal_ops) == len(local_gates) + 1
+    code = codes.ToricCode(2)
+    assert len(circuits.get_transversal_ops(code, [])) == 0
+    assert len(circuits.get_transversal_ops(code, ["SWAP"])) == 2
+    assert len(circuits.get_transversal_ops(code, ["SWAP", "H"])) == 3
+    assert len(circuits.get_transversal_ops(code, ["SWAP", "S"])) == 3
+    assert len(circuits.get_transversal_ops(code, ["SWAP", "SQRT_X"])) == 3
+    assert len(circuits.get_transversal_ops(code, ["SWAP", "H", "S"])) == 4
+
+    # non-self-dual [[8, 3, 2]] CSS code with nontrivial permutation automorphisms
+    code = codes.CSSCode(
+        [[1, 1, 1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1]],
+        [[1, 0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0, 1]],
+    )
+    assert len(circuits.get_transversal_ops(code, ["SWAP"])) == 3
 
     with pytest.raises(ValueError, match="Local Clifford gates"):
         circuits.get_transversal_automorphism_group(code, ["SQRT_Y"])
diff --git a/src/qldpc/external/groups.py b/src/qldpc/external/groups.py
index fe72cd6a3..d728de555 100644
--- a/src/qldpc/external/groups.py
+++ b/src/qldpc/external/groups.py
@@ -371,13 +371,15 @@ def get_primitive_central_idempotents(group: str, field: int) -> IdempotentsList
     "SmallGroup(1,1)": [[]],
     "Group(())": [[]],
     "SmallGroup(21,1)": [[(1, 2, 4), (3, 6, 5)], [(0, 1, 2, 3, 4, 5, 6)]],
+    # FiveQubitCode automorphism group (SWAP only)
     "AutomorphismGroup(CheckMatCode([[1,0,0,0,1,1,1,0,1,1],[0,1,0,0,1,0,0,1,1,0],[0,0,1,0,1,1,1,0,0,0],[0,0,0,1,1,1,0,1,1,1]],GF(2)))": [
         [(3, 7), (4, 5), (8, 9)],
         [(1, 5), (2, 7), (3, 9), (6, 8)],
         [(2, 6), (3, 8), (4, 5), (7, 9)],
         [(0, 9, 2, 8), (1, 6), (3, 5, 4, 7)],
         [(0, 7, 3), (1, 9, 8), (2, 4, 5)],
-    ],  # FiveQubitCode automorphism group (SWAP only)
+    ],
+    # FiveQubitCode automorphism group (SWAP + Cliffords)
     "AutomorphismGroup(CheckMatCode([[1,0,0,0,1,1,1,0,1,1,0,1,0,1,0],[0,1,0,0,1,0,0,1,1,0,0,1,1,1,1],[0,0,1,0,1,1,1,0,0,0,1,1,1,0,1],[0,0,0,1,1,1,0,1,1,1,1,0,1,0,0]],GF(2)))": [
         [(0, 1), (5, 12), (6, 14), (7, 9)],
         [(2, 3), (6, 9), (7, 14), (8, 11)],
@@ -388,12 +390,14 @@ def get_primitive_central_idempotents(group: str, field: int) -> IdempotentsList
         [(2, 11), (3, 8), (6, 14), (7, 9)],
         [(3, 8), (4, 10), (5, 12), (7, 9)],
         [(3, 9), (4, 12), (5, 10), (7, 8)],
-    ],  # FiveQubitCode automorphism group (SWAP + Cliffords)
+    ],
+    # ToricCode(2) automorphism group (SWAP only)
     "AutomorphismGroup(CheckMatCode([[1,1,1,1]],GF(2)))": [
         [(0, 1)],
         [(1, 2)],
         [(2, 3)],
-    ],  # ToricCode(2) automorphism group (SWAP only)
+    ],
+    # ToricCode(2) automorphism group (SWAP + H/S/SQRT_X)
     "AutomorphismGroup(CheckMatCode([[1,1,1,1,0,0,0,0],[0,0,0,0,1,1,1,1]],GF(2)))": [
         [(2, 3), (4, 7), (5, 6)],
         [(4, 7, 6, 5)],
@@ -403,7 +407,8 @@ def get_primitive_central_idempotents(group: str, field: int) -> IdempotentsList
         [(1, 3), (4, 6), (5, 7)],
         [(0, 6, 3, 7), (1, 5), (2, 4)],
         [(0, 7), (1, 4), (2, 5, 3, 6)],
-    ],  # ToricCode(2) automorphism group (SWAP + H/S/SQRT_X)
+    ],
+    # ToricCode(2) automorphism group (SWAP + Cliffords)
     "AutomorphismGroup(CheckMatCode([[1,1,1,1,0,0,0,0,1,1,1,1],[0,0,0,0,1,1,1,1,1,1,1,1]],GF(2)))": [
         [(4, 9), (5, 8, 6, 11), (7, 10)],
         [(4, 7, 6, 5), (9, 11, 10)],
@@ -419,7 +424,28 @@ def get_primitive_central_idempotents(group: str, field: int) -> IdempotentsList
         [(0, 4, 10, 1, 5, 9, 2, 7, 8), (3, 6, 11)],
         [(2, 3), (4, 7), (8, 11)],
         [(0, 10, 2, 11, 1, 9), (3, 8), (4, 7)],
-    ],  # ToricCode(2) automorphism group (SWAP + Cliffords)
+    ],
+    # [[8, 3, 2]] X check automorphism group
+    "AutomorphismGroup(CheckMatCode([[1,1,0,0,0,0,1,1],[0,0,1,1,0,0,1,1],[0,0,0,0,1,1,1,1]],GF(2)))": [
+        [(6, 7)],
+        [(4, 5), (6, 7)],
+        [(4, 7, 5, 6)],
+        [(2, 3), (6, 7)],
+        [(2, 6, 4), (3, 7, 5)],
+        [(0, 3, 5, 1, 2, 4)],
+        [(0, 7), (1, 6), (2, 3), (4, 5)],
+    ],
+    # [[8, 3, 2]] Z check automorphism group
+    "AutomorphismGroup(CheckMatCode([[1,0,1,0,1,0,1,0],[0,1,0,1,0,1,0,1]],GF(2)))": [
+        [(1, 7), (3, 5), (4, 6)],
+        [(1, 7, 5, 3)],
+        [(5, 7)],
+        [(3, 5, 7)],
+        [(1, 3, 5), (2, 4, 6)],
+        [(1, 5), (2, 6), (3, 7)],
+        [(0, 5, 6, 7), (1, 4), (2, 3)],
+        [(0, 7), (1, 2), (3, 6, 5, 4)],
+    ],
 }
 
 KNOWN_PRIMITIVE_CENTRAL_IDEMPOTENTS: dict[tuple[str, int], IdempotentsList] = {