diff --git a/qutip/core/dimensions.py b/qutip/core/dimensions.py
index 56fe3539..1f2015ba 100644
--- a/qutip/core/dimensions.py
+++ b/qutip/core/dimensions.py
@@ -923,10 +923,19 @@ class Dimensions(metaclass=MetaDims):
         flatl = self.to_.flat()
         stepr = self.from_.step()
         flatr = self.from_.flat()
-        return tuple(np.concatenate([
-            np.array(flatl)[np.argsort(stepl)[::-1]],
-            np.array(flatr)[np.argsort(stepr)[::-1]],
-        ]))
+        if self.issuper and isinstance(self.to_, SuperSpace) and isinstance(self.from_, SuperSpace):
+            # For superoperators where both input and output are superoperators,
+            # the order of left and right indices is swapped to match
+            # column‑stacking convention.
+            return tuple(np.concatenate([
+                np.array(flatr)[np.argsort(stepr)[::-1]],
+                np.array(flatl)[np.argsort(stepl)[::-1]],
+            ]))
+        else:
+            return tuple(np.concatenate([
+                np.array(flatl)[np.argsort(stepl)[::-1]],
+                np.array(flatr)[np.argsort(stepr)[::-1]],
+            ]))
 
     def _get_tensor_perm(self):
         """
@@ -936,10 +945,19 @@ class Dimensions(metaclass=MetaDims):
         # dims_to_tensor_perm
         stepl = self.to_.step()
         stepr = self.from_.step()
-        return list(np.concatenate([
-            np.argsort(stepl)[::-1],
-            np.argsort(stepr)[::-1] + len(stepl)
-        ]))
+        if self.issuper and isinstance(self.to_, SuperSpace) and isinstance(self.from_, SuperSpace):
+            # For superoperators where both input and output are superoperators,
+            # the order of left and right indices is swapped to match
+            # column‑stacking convention.
+            return list(np.concatenate([
+                np.argsort(stepr)[::-1],
+                np.argsort(stepl)[::-1] + len(stepr)
+            ]))
+        else:
+            return list(np.concatenate([
+                np.argsort(stepl)[::-1],
+                np.argsort(stepr)[::-1] + len(stepl)
+            ]))
 
     def remove(self, idx: int | list[int]) -> "Dimensions":
         """