Dic₃×C₂²⋊H(3,𝔽₃) #13048455

order	1296
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₂×C₃²

Aliases

direct product	Dic₃×C₂²⋊H(3,𝔽₃)
unambiguous semidirect product	C₃⋊(C₄×C₂²⋊H(3,𝔽₃))
unambiguous semidirect product	(C₂²×Dic₃)⋊H(3,𝔽₃)
unambiguous semidirect product	(C₃²×Dic₃)⋊A₄
unambiguous semidirect product	(C₃×Dic₃×A₄)⋊C₃

316 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

μ_t(G) = 36

maximal subgroup of	#67×C₂²⋊H(3,𝔽₃), #72222928, #72222929, …
maximal normal subgroup of	#67×C₂²⋊H(3,𝔽₃), #72222928, #72222929, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2173);