FIX: Pull subgroups of TOM for lattice back through isomorphism

This bug likely did not show up earlier since the TOM library was not loaded
by default.

Even an example is provided, the latter thrice as error does not arise every
time.

This fixes #2586

lib/grplatt.gi

@@ -2819,11 +2819,10 @@ InstallGlobalFunction("SubgroupsTrivialFitting",function(G)
 	ValueOption(NO_PRECOMPUTED_DATA_OPTION)<>true then
       Info(InfoPerformance,2,"Using Table of Marks Library");
       go:=ImagesSource(tom[1]);
-      tom:=tom[2];
       Info(InfoLattice,1, "Fetching subgroups of simple ",
-	  Identifier(tom)," from table of marks");
-      len:=LengthsTom(tom);
-      sub:=List([1..Length(len)],x->RepresentativeTom(tom,x));
+	  Identifier(tom[2])," from table of marks");
+      len:=LengthsTom(tom[2]);
+      sub:=List([1..Length(len)],x->PreImage(tom[1],RepresentativeTom(tom[2],x)));
       return sub;
     fi;
   fi;
@@ -2851,14 +2850,15 @@ InstallGlobalFunction("SubgroupsTrivialFitting",function(G)
 	tom:=TomDataAlmostSimpleRecognition(i);
 	if tom<>fail then
 	  go:=ImagesSource(tom[1]);
-	  tom:=tom[2];
-	  if tom<>fail and
+	  if tom[2]<>fail and
 	   ValueOption(NO_PRECOMPUTED_DATA_OPTION)<>true then
 	    Info(InfoPerformance,2,"Using Table of Marks Library");
 	    Info(InfoLattice,1, "Fetching subgroups of simple ",
-	      Identifier(tom)," from table of marks");
-	    len:=LengthsTom(tom);
-	    sub:=List([1..Length(len)],x->RepresentativeTom(tom,x));
+	      Identifier(tom[2])," from table of marks");
+	    len:=LengthsTom(tom[2]);
+            # different than above -- no preimage. We're setting subgroups
+            # of go
+	    sub:=List([1..Length(len)],x->RepresentativeTom(tom[2],x));
 	    sub:=List(sub,x->ConjugacyClassSubgroups(go,x));
 	    SetConjugacyClassesSubgroups(go,sub);
 	  fi;
@@ -2869,7 +2869,6 @@ InstallGlobalFunction("SubgroupsTrivialFitting",function(G)
 	fi;
 	Add(gold,go);
 
-
 	p:=Length(types);
       fi;
       Add(iso,IsomorphismGroups(i,gold[p]));

tst/testbugfix/2018-06-28-grplatt.tst

@@ -0,0 +1,12 @@
+# verify fix for bug #2586 on GitHub
+
+gap> g:=TransitiveGroup(6,14);;
+gap> cl:=ConjugacyClassesSubgroups(g);;
+gap> ForAll(cl,x->IsSubset(g,Representative(x)));
+true
+gap> Length(ConjugacyClassesSubgroups(SmallGroup(120,5)));
+12
+gap> Length(ConjugacyClassesSubgroups(SmallGroup(120,5)));
+12
+gap> Length(ConjugacyClassesSubgroups(SmallGroup(120,5)));
+12