Subgroups — #66343

Order 324.

29 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉⋊D₉	C₂	1	1	yes	maximal, characteristic
2	C₉²	C₄	1	1	yes	characteristic, complemented, Sylow
3	C₃⋊D₉	—	6	2	no	—
4	#157	—	9	1	no	maximal
5	C₃×C₉	—	2	2	no	—
6	C₃⋊D₃	—	9	1	no	—
7	D₉	—	18	6	no	—
8	C₃²	#157	1	1	yes	characteristic
9	C₉	—	2	6	no	—
10	D₃	—	54	2	no	—
11	C₄	—	81	1	no	Sylow
12	C₃	—	2	2	no	—
13	C₂	—	81	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉²	C₄
Frattini, socle	C₃²	#157
prime radical, cosocle	C₉⋊D₉	C₂
LCS	G ▷ C₉²
UCS	C₁

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

N	H ≅ G/N	type
2. C₉²	C₄	semidirect

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

subgroup	index
C₉⋊D₉	2
#157	9