D₄×(C₃⋊D₃)⋊C₉ #13047337

order	1296
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂³×C₃

Aliases

direct product	D₄×(C₃⋊D₃)⋊C₉
unambiguous semidirect product	(D₄×C₃⋊D₃)⋊C₉

Fitting	D₄×C₃²⋊C₉ ⋊ C₂
Sylow	C₃²⋊C₉ ⋊ C₂×D₄

345 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 345 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

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

μ_t(G) = 72

maximal subgroup of	D₄×#92259, D₄×((C₃⋊D₃)⋊C₉)⋊C₂
maximal normal subgroup of	D₄×#92259, D₄×((C₃⋊D₃)⋊C₉)⋊C₂

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1055);