C₂×#11722391 #13164494

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³×C₃

Aliases

	subgroup	G/H
center	C₂²	C₂×C₃⋊((C₂²⋊C₉)⋊C₂)
commutator, cosocle, hypocenter	C₃×Q₈⋊C₉	C₂³
Frattini	C₂×C₃	C₂²×C₃⋊S₄
Fitting	C₂×C₃²×#41	D₃
socle	C₂²×C₃²	C₂×S₄
hypercenter	C₂×C₄	C₃⋊((C₂²⋊C₉)⋊C₂)
LCS	G ▷ C₃×Q₈⋊C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄

928 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 928 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

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

μ_t(G) = 432

maximal subgroup of	C₂×#13147076, C₂×#72252949
maximal normal subgroup of	C₂×#13147076, C₂×#72252949

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 30557);