C₂×#72212847 #72267162

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁸

Aliases

	subgroup	G/H
center	C₂²	C₂×#87588
commutator, cosocle, hypocenter	C₂²⋊(C₂²⋊SL(2,𝔽₃))	C₂³
Frattini	C₂	C₂²×#87588
Fitting	C₂⁵×#41	D₃
socle	C₂⁶	C₂×S₄
prime radical	C₂×#11710913	C₂
hypercenter	C₂×C₄	#87588
LCS	G ▷ C₂²⋊(C₂²⋊SL(2,𝔽₃))
UCS	C₁ ◁ C₂² ◁ C₂×C₄

92226 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 92226 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

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

μ_t(G) = 96

maximal subgroup of	C₂×#72212876
maximal normal subgroup of	C₂×#72212876

Past the SmallGroups library coverage — no SmallGroups id.