Subgroups — #20266483⋊C₃ #34085577

Order 19452.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆₂₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#20266483	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₆₂₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₆₂₁	C₂×C₃	1	1	yes	characteristic
5	C₁₆₂₁	C₃×C₄	1	1	yes	characteristic, complemented, Sylow
6	C₃×C₄	—	1621	1	no	maximal, Hall
7	C₂×C₃	—	1621	1	no	—
8	C₄	—	1621	1	no	Sylow
9	C₃	—	6484	1	no	Sylow
10	C₂	—	1621	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₆₂₁	C₃×C₄
prime radical	D₁₆₂₁⋊C₃	C₂
cosocle	D₁₆₂₁	C₂×C₃
LCS	G ▷ C₁₆₂₁
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.