C₂²×C₃⋊((C₂²⋊C₉)⋊C₂) #11724047

order	864
isoclinism	isoclinic class of C₃⋊((C₂²⋊C₉)⋊C₂)
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁴×C₃

Aliases

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊((C₂²⋊C₉)⋊C₂)
commutator, cosocle, hypocenter	C₃×C₂²⋊C₉	C₂³
Frattini	C₃	C₂²×C₃⋊S₄
Fitting, socle	C₂⁴×C₃²	D₃
LCS	G ▷ C₃×C₂²⋊C₉
UCS	C₁ ◁ C₂²

722 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

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

μ_t(G) = 108

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 4014);