Subgroups — #92204

Order 486.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6862	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	#4169	—	3	4	no	maximal
3	C₃²⋊C₉	D₃	1	4	yes	—
4	C₃×C₃⋊D₃	—	9	1	no	—
5	C₃⋊D₉	—	3	4	no	—
6	C₃³	C₃⋊D₃	1	1	yes	characteristic
7	C₃×C₉	—	3	4	no	—
8	C₃⋊D₃	—	9	1	no	—
9	C₃×D₃	—	27	4	no	—
10	D₉	—	27	4	no	—
11	C₃²	—	3	4	no	—
12	C₃²	#272	1	1	yes	characteristic
13	C₉	—	9	4	no	—
14	C₂×C₃	—	81	1	no	—
15	D₃	—	27	4	no	—
16	C₃	—	9	1	no	—
17	C₃	#4184	1	4	yes	—
18	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#6862	C₂
Frattini	C₃³	C₃⋊D₃
socle	C₃²	#272
LCS	G ▷ #6862
UCS	C₁

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

N	H ≅ G/N	type
1. #6862	C₂	semidirect

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

subgroup	index
#6862	2
#4169	3