C₃⋊D₃×GU(2,𝔽₃) #13165977

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₄	C₃⋊D₃×S₄
commutator, hypocenter	C₃²×SL(2,𝔽₃)	C₂×C₄
Fitting	C₃²×#41	C₂×D₃
socle	C₂×C₃²	C₂×SL(2,ℤ/4)
prime radical	C₃⋊D₃×#41⋊C₃	C₂
cosocle	C₃²×#41⋊C₃	C₂²
LCS	G ▷ C₃²×SL(2,𝔽₃)
UCS	C₁ ◁ C₄

542 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

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

μ_t(G) = 216

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 32040);