Subgroups — #92162

Order 486.

59 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6857	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊#272	C₃	1	1	yes	maximal, characteristic
3	(C₃⋊D₃)⋊C₉	—	3	1	no	maximal
4	C₃×3₋¹⁺²	—	2	1	no	—
5	C₃×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
6	C₃²⋊C₉	D₃	1	1	yes	characteristic, complemented
7	C₃×C₃⋊D₃	—	3	1	no	—
8	C₃×C₃⋊D₃	—	9	1	no	—
9	#272	—	9	3	no	—
10	D₃×C₉	—	9	1	no	—
11	C₃³	—	3	1	no	—
12	C₃³	C₃×D₃	1	1	yes	characteristic
13	3₋¹⁺²	—	6	3	no	—
14	H(3,𝔽₃)	—	3	3	no	—
15	C₃×C₉	—	3	1	no	—
16	C₃×C₉	—	6	1	no	—
17	C₃⋊D₃	—	3	1	no	—
18	C₃⋊D₃	—	9	1	no	—
19	C₃×D₃	—	9	1	no	—
20	C₃×D₃	—	27	1	no	—
21	C₃×D₃	—	27	3	no	—
22	C₂×C₉	—	27	1	no	—
23	C₃²	—	3	1	no	—
24	C₃²	—	3	3	no	—
25	C₃²	—	3	1	no	—
26	C₃²	—	6	1	no	—
27	C₃²	—	9	1	no	—
28	C₃²	—	18	1	no	—
29	C₃²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
30	C₉	—	6	3	no	—
31	C₉	—	9	1	no	—
32	C₂×C₃	—	27	1	no	—
33	D₃	—	9	1	no	—
34	D₃	—	27	1	no	—
35	D₃	—	27	3	no	—
36	C₃	—	2	1	no	—
37	C₃	—	9	1	no	—
38	C₃	—	9	3	no	—
39	C₃	#4175	1	1	yes	characteristic
40	C₃	#4176	1	1	yes	characteristic
41	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#4175
commutator, cosocle, hypocenter	C₃×H(3,𝔽₃)	C₂×C₃
Frattini	C₃³	C₃×D₃
Fitting	#6857	C₂
socle	C₃²	(C₃⋊D₃)⋊C₃
prime radical	C₃⋊#272	C₃
LCS	G ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₃

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

N	H ≅ G/N	type
1. #6857	C₂	semidirect
6. C₃²⋊C₉	D₃	semidirect

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