U:=( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19);
L:=( 9,11,16,14)(10,13,15,12)( 1,17,41,40)( 4,20,44,37)( 6,22,46,35);
F:= (17,19,24,22)(18,21,23,20)( 6,25,43,16)( 7,28,42,13)( 8,30,41,11);
R:=(25,27,32,30)(26,29,31,28)( 3,38,43,19)( 5,36,45,21)( 8,33,48,24);
B:=(33,35,40,38)(34,37,39,36)( 3, 9,46,32)( 2,12,47,29)( 1,14,48,27);
D:=(41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40);

cube := Group(U,L,F,R,B,D);;
twist_subgroup:=Group(U*R^(-1),U*D^(-1),U*L^(-1),U*F^(-1),U*B^(-1),
R*D^(-1),R*L^(-1),R*F^(-1),R*B^(-1),
B*L^(-1),B*D^(-1),D*F^(-1),D*L^(-1));;
square_group := Group(U^2,L^2,F^2,R^2,B^2,D^2);;

ans:=IsSimple(twist_subgroup);

N1:= Size( cube );
Collected( Factors(N1) );

N2:=Size(twist_subgroup);
Collected( Factors(N2) );

N3:=Size(square_group);
Collected( Factors(N3) );