Trying to add subgroup lattice into my PermGroup page
(http://wims.unice.fr/~wims/en_tool~algebra~permgroup.en.phtml), I got
the following output from GAP which I am unable to interprete.

--------------------------------------------
gap> g:=SmallGroup(18,3);
<pc group of size 18 with 3 generators>
gap> l:=LatticeSubgroups(g);
LatticeSubgroups(Group( [ f1, f2, f3 ] ),# 9 classes, 14 subgroups)
gap> c:=List(ConjugacyClassesSubgroups(g),Representative);
[ Group([  ]), Group([ f3 ]), Group([ f2 ]), Group([ f2*f3 ]),
  Group([ f2, f3 ]), Group([ f2, f3, f1 ]), Group([ f1 ]), Group([ f1,
f3 ]),
  Group([ f1, f2 ]) ]
gap> List(c,Size);
[ 1, 3, 3, 3, 9, 18, 2, 6, 6 ]
gap> MaximalSubgroupsLattice(l);
[ [  ], [ [ 1, 1 ] ], [ [ 1, 1 ] ], [ [ 1, 1 ] ],
  [ [ 4, 1 ], [ 4, 2 ], [ 3, 1 ], [ 2, 1 ] ], [ [ 5, 1 ] ], [ [ 1, 1 ]
],
  [ [ 7, 1 ], [ 7, 2 ], [ 7, 3 ], [ 2, 1 ] ], [ [ 8, 1 ], [ 6, 1 ] ] ]
gap>       
--------------------------------------------

The output seems to tell that the class #6, or order 6, has class #6
which is the whole group, as a maximal subgroup. What is wrong?

-- 

XIAO Gang (~{P$8U~})                          xiao@unice.fr
               http://pcmath126.unice.fr/xiao.html

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