gap> uu:=(1,3)(2,4);ff:=(1,8)(4,5);dd:=(5,7)(6,8);
(1,3)(2,4)
(1,8)(4,5)
(5,7)(6,8)
gap> bb:=(3,6)(2,7);rr:=(2,5)(1,6);ll:=(4,7)(3,8);
(2,7)(3,6)
(1,6)(2,5)
(3,8)(4,7)
gap> H:=Group(uu,ff,rr,dd,bb,ll);
Group( (1,3)(2,4), (1,8)(4,5), (1,6)(2,5), (5,7)(6,8), (2,7)(3,6), (3,8)
(4,7) )
gap> H1:=Stabilizer(H,1);
Subgroup( Group( (1,3)(2,4), (1,8)(4,5), (1,6)(2,5), (5,7)(6,8), (2,7)(3,6), 
(3,8)(4,7) ), [ (5,7)(6,8), (2,7)(3,6), (3,8)(4,7) ] )
gap> Size(H1);
24
gap> L1:=Lattice(H1);
LatticeSubgroups( Subgroup( Group( (1,3)(2,4), (1,8)(4,5), (1,6)(2,5), (5,7)
(6,8), (2,7)(3,6), (3,8)(4,7) ), [ (5,7)(6,8), (2,7)(3,6), (3,8)(4,7) ] ) )
gap> N1:=NormalSubgroups(H1);
[ Subgroup( Group( (1,3)(2,4), (1,8)(4,5), (1,6)(2,5), (5,7)(6,8), (2,7)
    (3,6), (3,8)(4,7) ), [  ] ), Subgroup( Group( (1,3)(2,4), (1,8)(4,5), 
    (1,6)(2,5), (5,7)(6,8), (2,7)(3,6), (3,8)(4,7) ), 
    [ (2,4)(5,7), (2,5)(4,7) ] ), Subgroup( Group( (1,3)(2,4), (1,8)(4,5), 
    (1,6)(2,5), (5,7)(6,8), (2,7)(3,6), (3,8)(4,7) ), 
    [ (3,6,8)(4,5,7), (2,4,5)(3,8,6) ] ), Subgroup( Group( (1,3)(2,4), (1,8)
    (4,5), (1,6)(2,5), (5,7)(6,8), (2,7)(3,6), (3,8)(4,7) ), 
    [ (5,7)(6,8), (2,5)(3,8), (3,6)(4,5) ] ) ]
gap> Size(N1[1]);
1
gap> Size(N1[2]);
4
gap> Size(N1[3]);
12
gap> Size(N1[4]);
24
gap> Size(N1[5]);
Error, List Element: <list>[5] must have a value
gap> H2:=Stabilizer(H,2);
Subgroup( Group( (1,3)(2,4), (1,8)(4,5), (1,6)(2,5), (5,7)(6,8), (2,7)(3,6), 
(3,8)(4,7) ), [ (5,7)(6,8), (3,8)(4,7), (1,6,8,3)(4,5) ] )
gap> Intersection(H1,H2);
Subgroup( Group( (1,3)(2,4), (1,8)(4,5), (1,6)(2,5), (5,7)(6,8), (2,7)(3,6), 
(3,8)(4,7) ), [ (5,7)(6,8), (3,8)(4,7) ] )
gap> H12:=Intersection(H1,H2);
Subgroup( Group( (1,3)(2,4), (1,8)(4,5), (1,6)(2,5), (5,7)(6,8), (2,7)(3,6), 
(3,8)(4,7) ), [ (5,7)(6,8), (3,8)(4,7) ] )
gap> Size(H12);
6
gap> IsConjugateSubgroup(H1,H2);
Error, Variable: 'IsConjugateSubgroup' must have a value
gap> ConjugateSubgroup(H1,H2);
Error, <g> must be an element of the parent group of <G> in
ConjugateSubgroup( H1, H2 ) called from
main loop
brk> quit;
gap> Size(H2);
24
gap> H3:=Stabilizer(H,3);
Subgroup( Group( (1,3)(2,4), (1,8)(4,5), (1,6)(2,5), (5,7)(6,8), (2,7)(3,6), 
(3,8)(4,7) ), [ (5,7)(6,8), (1,8)(2,7), (1,6,8)(2,4,5) ] )
gap> H123:=Intersection(H12,H3);
Subgroup( Group( (1,3)(2,4), (1,8)(4,5), (1,6)(2,5), (5,7)(6,8), (2,7)(3,6), 
(3,8)(4,7) ), [ (5,7)(6,8) ] )
gap> Size(H123);
2
gap> quit;