D₃×#92394 #72243726

order	2916
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

C₃×3₋¹⁺⁴ ⋊ C₂²

	subgroup	G/H
center, Frattini	C₃	C₃²×D₃×C₃⋊D₃
commutator, cosocle, hypocenter	C₃×H(3,𝔽₃)	C₂²×C₃²
Fitting	C₃×3₋¹⁺⁴	C₂²
socle	C₃²	C₂×C₃²×C₃⋊D₃
prime radical	C₃×D₃×#272	C₃
hypercenter	3₋¹⁺²	D₃×C₃⋊D₃
LCS	G ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₃ ◁ 3₋¹⁺²

1590 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 1590 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

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

μ_t(G) = 54

maximal subgroup of	#72243729, D₃×#13091661, #72243831, …
maximal normal subgroup of	D₃×#13091661, D₃×(#4207⋊C₂)⋊C₃

Past the SmallGroups library coverage — no SmallGroups id.