D₃×#63731 #13165162

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃×GO⁺(4,𝔽₂)
commutator	C₃×C₃⋊Dic₃	C₂²×C₄
Fitting	C₃³×C₄	C₂×D₄
socle	C₂×C₃³	C₂×C₂²⋊C₄
prime radical	D₃×#3798	C₂
cosocle	C₃×C₄×C₃⋊D₃	C₂³
hypocenter	C₃³	C₂×#104
LCS	G ▷ C₃×C₃⋊Dic₃ ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₄

632 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

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

μ_t(G) = 96

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 31225);