Subgroups — C₂²⋊C₉ #151

Order 36.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃	C₃	1	1	yes	maximal, characteristic
2	C₉	—	4	1	no	maximal, Sylow
3	C₂×C₃	—	3	1	no	—
4	C₂²	C₉	1	1	yes	characteristic, complemented, Sylow
5	C₃	A₄	1	1	yes	characteristic
6	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	A₄
commutator, hypocenter	C₂²	C₉
Fitting, socle, prime radical, cosocle	C₂²×C₃	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃

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

N	H ≅ G/N	type
4. C₂²	C₉	semidirect

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

subgroup	index
C₂²×C₃	3
C₉	4