D₃×#92281 #72243723

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

Aliases

	subgroup	G/H
center	C₃	C₃×D₃×(C₃⋊D₃)⋊C₃
commutator, cosocle, hypocenter	C₃×H(3,𝔽₃)	C₂²×C₃²
Frattini	C₃²	C₃²×D₃²
Fitting	C₃×#6909	C₂²
socle	C₃²	C₂×C₃×(C₃⋊D₃)⋊C₃
hypercenter	C₃²	D₃×(C₃⋊D₃)⋊C₃
LCS	G ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₃ ◁ C₃²

645 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 645 conjugacy classes of subgroups — too many to draw. Only its 69 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	#72243728, #72243734, #72243738, …
maximal normal subgroup of	D₃×#13091645, D₃×(#4174⋊C₂)⋊C₃

Past the SmallGroups library coverage — no SmallGroups id.