C₂×D₃²×H(3,𝔽₃) #14519299

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂³×C₃²

Aliases

direct product	C₂×D₃²×H(3,𝔽₃)
unambiguous semidirect product	(C₃×D₃)⋊(C₂²×H(3,𝔽₃))
unambiguous semidirect product	(C₂×C₃²×D₃²)⋊C₃

Fitting	C₂×C₃²×H(3,𝔽₃) ⋊ C₂²
Sylow	C₃²×H(3,𝔽₃) ⋊ C₂³

1223 conjugacy classes of subgroups; only the 196 normal subgroups are shown.

normal subgroups only

This group has 1223 conjugacy classes of subgroups — too many to draw. Only its 196 normal subgroups are shown.

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

μ_t(G) = 72

maximal subgroup of	C₂×D₃²×(C₃⋊D₃)⋊C₃
maximal normal subgroup of	C₂×D₃²×(C₃⋊D₃)⋊C₃

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3693);