diff --git a/src/sage/groups/libgap_wrapper.pyx b/src/sage/groups/libgap_wrapper.pyx
index e0113e4bd17..4abe634a74c 100644
--- a/src/sage/groups/libgap_wrapper.pyx
+++ b/src/sage/groups/libgap_wrapper.pyx
@@ -357,7 +357,8 @@ class ParentLibGAP(SageObject):
              [0 6]
              ) of Special Linear Group of degree 2 over Finite Field in z2 of size 7^2]
         """
-        return [self._subgroup_constructor(gap_subgroup) for gap_subgroup in self.gap().MinimalNormalSubgroups()]
+        return [self._subgroup_constructor(gap_subgroup)
+                for gap_subgroup in self._libgap().MinimalNormalSubgroups()]
 
     def maximal_normal_subgroups(self):
         """
@@ -374,7 +375,8 @@ class ParentLibGAP(SageObject):
              [0 6]
              ) of Special Linear Group of degree 2 over Finite Field in z2 of size 7^2]
         """
-        return [self._subgroup_constructor(gap_subgroup) for gap_subgroup in self.gap().MaximalNormalSubgroups()]
+        return [self._subgroup_constructor(gap_subgroup)
+                for gap_subgroup in self._libgap().MaximalNormalSubgroups()]
 
     @cached_method
     def gens(self):
diff --git a/src/sage/groups/perm_gps/permgroup.py b/src/sage/groups/perm_gps/permgroup.py
index 139e7ca7fb7..ef828055b6a 100644
--- a/src/sage/groups/perm_gps/permgroup.py
+++ b/src/sage/groups/perm_gps/permgroup.py
@@ -4108,7 +4108,7 @@ def isomorphism_type_info_simple_group(self):
 
     def minimal_normal_subgroups(self):
         """
-        Return a list containing those nontrivial normal subgroups of the group that are minimal among the nontrivial normal subgroups.
+        Return the nontrivial minimal normal subgroups ``self``.
 
         EXAMPLES::
 
@@ -4117,12 +4117,15 @@ def minimal_normal_subgroups(self):
             [Subgroup generated by [(4,5)] of (Permutation Group with generators [(4,5), (1,2,3)]),
              Subgroup generated by [(1,2,3)] of (Permutation Group with generators [(4,5), (1,2,3)])]
         """
-        return [self.subgroup(gap_group=gap_subgroup) for gap_subgroup in self.gap().MinimalNormalSubgroups()]
+        return [self.subgroup(gap_group=gap_subgroup)
+                for gap_subgroup in self._libgap_().MinimalNormalSubgroups()]
 
     def maximal_normal_subgroups(self):
         """
-        Return a list containing those proper normal subgroups of the group G that are maximal among the proper normal subgroups.
-        Gives error if G/G' is infinite, yielding infinitely many maximal normal subgroups.
+        Return the maximal proper normal subgroups of ``self``.
+
+        This raises an error if `G/[G, G]` is infinite, yielding infinitely
+        many maximal normal subgroups.
 
         EXAMPLES::
 
@@ -4131,7 +4134,8 @@ def maximal_normal_subgroups(self):
             [Subgroup generated by [(1,2,3)] of (Permutation Group with generators [(4,5), (1,2,3)]),
              Subgroup generated by [(4,5)] of (Permutation Group with generators [(4,5), (1,2,3)])]
         """
-        return [self.subgroup(gap_group=gap_subgroup) for gap_subgroup in self.gap().MaximalNormalSubgroups()]
+        return [self.subgroup(gap_group=gap_subgroup)
+                for gap_subgroup in self._libgap_().MaximalNormalSubgroups()]
 
     ######################  Boolean tests #####################