S₄×C₂₇⋊C₃ #14517957

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	S₄×C₂₇⋊C₃
unambiguous semidirect product	A₄⋊(C₂×C₂₇⋊C₃)
unambiguous semidirect product	(S₄×C₂₇)⋊C₃

C₂²×C₂₇⋊C₃ ⋊ D₃

168 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

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

μ_t(G) = 108

maximal subgroup of	S₄×#6875, S₄×D₂₇⋊C₃
maximal normal subgroup of	S₄×#6875, S₄×D₂₇⋊C₃

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2351);