diff --git a/lib/stbcbckt.gi b/lib/stbcbckt.gi
index bc74f80f58..cf06f8980a 100644
--- a/lib/stbcbckt.gi
+++ b/lib/stbcbckt.gi
@@ -2671,6 +2671,9 @@ Eh, Lh, Nh,G0;
     L := arg[ 3 ];
     issub:=fail;
   elif IsSubset( G, E )   then
+    if Size(G)=Size(E) then
+      return G;
+    fi;
     L := E;
     issub:=true;
   else
@@ -2678,6 +2681,12 @@ Eh, Lh, Nh,G0;
     issub:=false;;
   fi;
 
+  if issub and HasFittingFreeLiftSetup(G) and NrMovedPoints(G)>1000
+    # radical is at lest 3rd root of |G| -- avoid smallish radical
+    and Size(FittingFreeLiftSetup(G).radical)^3>Size(G) then
+    return NormalizerViaRadical(G,E);
+  fi;
+
   mpG:=MovedPoints(GeneratorsOfGroup(G));
   mpE:=MovedPoints(GeneratorsOfGroup(E));
   if IsSubset(mpG,mpE) and not IsTransitive(G,mpG) then