C₃²×#5930 #13181414

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂²×C₃

Aliases

	subgroup	G/H
center, hypercenter	C₂×C₃²	#1020
commutator, cosocle, hypocenter	C₂²⋊SL(2,𝔽₃)	C₂×C₃²
Frattini	C₂	C₃²×#1020
Fitting	C₂²×C₃²×Q₈	D₃
socle	C₂³×C₃²	S₄
prime radical	C₃²×C₂²⋊SL(2,𝔽₃)	C₂
LCS	G ▷ C₂²⋊SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃²

456 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

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

μ_t(G) = 432

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47477);