diff --git a/lib/clashom.gi b/lib/clashom.gi
index e4844ec413..ffdb11559e 100644
--- a/lib/clashom.gi
+++ b/lib/clashom.gi
@@ -2391,8 +2391,15 @@ local r,	#radical
       hom:=ser.factorhom;
       ntrihom:=true;
       f:=Image(hom);
+      # if lift setup is inherited, f might not be trivial-fitting
+      if Size(RadicalGroup(f))>1 then
+        # this is proper recursion
+        cl:=ConjugacyClasses(f:onlysizes:=false);
+        cl:=List(cl,x->[Representative(x),Centralizer(x)]);
+      else
       # we need centralizers
-      cl:=ConjugacyClassesFittingFreeGroup(f:onlysizes:=false);
+        cl:=ConjugacyClassesFittingFreeGroup(f:onlysizes:=false);
+      fi;
       fants:=Filtered(NormalSubgroups(f),x->Size(x)>1 and Size(x)<Size(f));
     else
       if IsPermGroup(G) then
diff --git a/tst/testbugfix/2018-12-30-clashom.tst b/tst/testbugfix/2018-12-30-clashom.tst
new file mode 100644
index 0000000000..c17218a965
--- /dev/null
+++ b/tst/testbugfix/2018-12-30-clashom.tst
@@ -0,0 +1,5 @@
+# Bug #3139
+gap> wreathy := WreathProduct(SymmetricGroup(2),SymmetricGroup(5));;
+gap> classes := ConjugacyClasses(wreathy);;
+gap> badsubgroup := StabilizerOfExternalSet( classes[2] );;
+gap> ConjugacyClasses( badsubgroup );;