D₃×#64265 #13180822

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³×C₃

Aliases

	subgroup	G/H
center, Frattini	C₂	C₂×D₃×C₃⋊S₄
commutator, cosocle, hypocenter	C₃²×SL(2,𝔽₃)	C₂³
Fitting	C₃²×#41	C₂×D₃
socle	C₂×C₃²	C₂²×S₄
prime radical	C₃×D₃×#41⋊C₃	C₂
hypercenter	C₄	D₃×C₃⋊S₄
LCS	G ▷ C₃²×SL(2,𝔽₃)
UCS	C₁ ◁ C₂ ◁ C₄

806 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

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

μ_t(G) = 192

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46885);