Subgroups — #92178

Order 486.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6868	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₉×C₃⋊D₃	—	3	1	no	maximal
3	#4181	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₉	D₃	1	1	yes	characteristic
5	C₃²⋊C₉	—	2	1	no	—
6	C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic
7	C₃×C₃⋊D₃	—	3	1	no	—
8	D₃×C₉	—	9	1	no	—
9	D₃×C₉	—	9	2	no	—
10	D₃×C₉	—	9	1	no	—
11	C₃×D₉	—	9	1	no	—
12	C₃³	C₃×D₃	1	1	yes	characteristic
13	C₃×C₉	—	2	1	no	—
14	C₃×C₉	—	3	1	no	—
15	C₃×C₉	—	3	2	no	—
16	C₃×C₉	—	3	1	no	—
17	C₃×C₉	—	6	1	no	—
18	C₃×C₉	D₉	1	1	yes	characteristic, complemented
19	C₃⋊D₃	—	3	1	no	—
20	C₃×D₃	—	9	1	no	—
21	C₃×D₃	—	9	1	no	—
22	C₃×D₃	—	9	2	no	—
23	C₂×C₉	—	27	1	no	—
24	D₉	—	9	1	no	—
25	C₃²	—	3	1	no	—
26	C₃²	—	6	1	no	—
27	C₃²	C₃×D₉	1	1	yes	characteristic
28	C₃²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
29	C₃²	AGL(1,ℤ/9)	1	2	yes	—
30	C₉	—	3	1	no	—
31	C₉	—	6	1	no	—
32	C₉	—	9	1	no	—
33	C₉	—	18	1	no	—
34	C₂×C₃	—	27	1	no	—
35	D₃	—	9	1	no	—
36	D₃	—	9	2	no	—
37	D₃	—	9	1	no	—
38	C₃	—	2	1	no	—
39	C₃	—	3	1	no	—
40	C₃	—	3	2	no	—
41	C₃	#4169	1	1	yes	characteristic
42	C₃	#4178	1	1	yes	characteristic
43	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#4169
commutator, cosocle, hypocenter	C₃²⋊C₉	C₂×C₃
Frattini	C₃³	C₃×D₃
Fitting	#6868	C₂
socle	C₃²	(C₃⋊D₃)⋊C₃
prime radical	#4181	C₃
LCS	G ▷ C₃²⋊C₉
UCS	C₁ ◁ C₃

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

N	H ≅ G/N	type
1. #6868	C₂	semidirect
18. C₃×C₉	D₉	semidirect

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