C₃×D₄×Q₈⋊C₉ #13152193

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

Aliases

direct product	C₃×D₄×Q₈⋊C₉
unambiguous semidirect product	C₄⋊(C₂×C₃×Q₈⋊C₉)
unambiguous semidirect product	(C₃×D₄×Q₈)⋊C₉

D₄×Q₈ ⋊ C₃×C₉

560 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.

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

μ_t(G) = 864

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18256);