Subgroups — #92197

Order 486.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6855	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊D₉	—	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	C₃×D₉	—	9	12	no	—
7	C₃³	C₃⋊D₃	1	1	yes	characteristic
8	C₃×C₉	—	3	4	no	—
9	C₃×C₉	—	6	4	no	—
10	C₃×C₉	D₉	1	12	yes	complemented
11	C₃⋊D₃	—	9	1	no	—
12	C₃×D₃	—	27	4	no	—
13	D₉	—	9	12	no	—
14	C₃²	—	2	4	no	—
15	C₃²	C₃⋊D₉	1	4	yes	—
16	C₃²	#272	1	1	yes	characteristic
17	C₉	—	3	12	no	—
18	C₂×C₃	—	81	1	no	—
19	D₃	—	27	4	no	—
20	C₃	—	2	4	no	—
21	C₃	C₉⋊D₉	1	1	yes	characteristic
22	C₃	#4181	1	4	yes	—
23	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₉⋊D₉
commutator, Fitting, cosocle, hypocenter	#6855	C₂
Frattini, socle	C₃³	C₃⋊D₃
LCS	G ▷ #6855
UCS	C₁ ◁ C₃

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

N	H ≅ G/N	type
1. #6855	C₂	semidirect
10. C₃×C₉	D₉	semidirect

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

subgroup	index
#6855	2
C₃×C₃⋊D₉	3