C₂²×D₃×Q₈⋊C₉ #13164616

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂²×D₃×Q₈⋊C₉
unambiguous semidirect product	C₃⋊(C₂³×Q₈⋊C₉)
unambiguous semidirect product	(C₂×C₃)⋊(C₂²×Q₈⋊C₉)

C₃×Q₈ ⋊ C₂³×C₉

1015 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1015 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.

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

μ_t(G) = 576

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 30679);