C₃×C₄⋊C₄×C₂²⋊C₉ #13152166

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄×C₉ · Schur multiplier (H₂) = C₂²×C₃

Aliases

direct product	C₃×C₄⋊C₄×C₂²⋊C₉
unambiguous semidirect product	C₄⋊(C₃×C₄×C₂²⋊C₉)
unambiguous semidirect product	(C₂²×C₃×C₄⋊C₄)⋊C₉

626 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 432

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18229);