#624×PSU(3,𝔽₂) #72259602

order	5184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₃

Aliases

C₃⁴ ⋊ C₂×C₄×Q₈

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃²×PSU(3,𝔽₂)
commutator	C₃²×C₃⋊D₃	C₂³×C₄
Fitting, socle	C₂×C₃⁴	C₂²×Q₈
prime radical	C₂×C₃⋊D₃²	C₂³
cosocle	C₂×C₃²×C₃⋊D₃	C₂⁴
hypocenter	C₃⁴	C₂×C₄×Q₈
LCS	G ▷ C₃²×C₃⋊D₃ ▷ C₃⁴
UCS	C₁ ◁ C₂

1571 conjugacy classes of subgroups; only the 236 normal subgroups are shown.

normal subgroups only

This group has 1571 conjugacy classes of subgroups — too many to draw. Only its 236 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	#624×PSU(3,𝔽₂)⋊C₃
maximal normal subgroup of	#624×PSU(3,𝔽₂)⋊C₃

Past the SmallGroups library coverage — no SmallGroups id.