Subgroups — C₂²⋊(C₁₆₂₁⋊C₃) #34085582

Order 19452.

10 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆₂₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₆₂₁⋊C₃	—	4	1	no	maximal, Hall
3	C₂×C₁₆₂₁	—	3	1	no	—
4	C₁₆₂₁	A₄	1	1	yes	characteristic, complemented, Sylow
5	A₄	—	1621	1	no	maximal, Hall
6	C₂²	C₁₆₂₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
7	C₃	—	6484	1	no	Sylow
8	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₁₆₂₁	C₃
LCS	G ▷ C₂²×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.