Subgroups — ((C₃⋊D₃)⋊C₉)⋊C₂ #66345

Order 324.

67 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4181	C₂	1	1	yes	maximal, characteristic, complemented
2	#4169	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₃⋊D₃)⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1113	—	3	1	no	maximal
5	D₃×D₉	—	3	1	no	maximal
6	C₃²⋊C₉	C₂²	1	1	yes	characteristic, complemented, Sylow
7	C₃×C₃⋊D₃	—	3	1	no	—
8	C₃×C₃⋊D₃	—	3	1	no	—
9	C₃×C₃⋊D₃	D₃	1	1	yes	characteristic
10	C₃⋊D₉	D₃	1	1	yes	characteristic, complemented
11	D₃×C₉	—	3	1	no	—
12	C₃×D₉	—	3	1	no	—
13	C₃×D₉	—	6	1	no	—
14	D₃²	—	9	1	no	—
15	D₃²	—	9	1	no	—
16	D₃²	—	9	1	no	—
17	C₂×D₉	—	9	1	no	—
18	C₃³	C₂×D₃	1	1	yes	characteristic
19	C₃×C₉	—	2	1	no	—
20	C₃×C₉	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃⋊D₃	—	3	1	no	—
22	C₃⋊D₃	—	3	1	no	—
23	C₃⋊D₃	D₉	1	1	yes	characteristic, complemented
24	C₃×D₃	—	3	1	no	—
25	C₃×D₃	—	9	1	no	—
26	C₃×D₃	—	9	1	no	—
27	C₃×D₃	—	9	1	no	—
28	C₃×D₃	—	9	1	no	—
29	C₃×D₃	—	9	1	no	—
30	C₃×D₃	—	18	1	no	—
31	C₃×D₃	—	18	1	no	—
32	C₂×C₉	—	9	1	no	—
33	D₉	—	3	1	no	—
34	D₉	—	6	1	no	—
35	D₉	—	9	1	no	—
36	C₂×D₃	—	27	1	no	—
37	C₂×D₃	—	27	1	no	—
38	C₂×D₃	—	27	1	no	—
39	C₃²	—	2	1	no	—
40	C₃²	—	3	1	no	—
41	C₃²	—	6	1	no	—
42	C₃²	C₂×D₉	1	1	yes	characteristic, complemented
43	C₃²	D₃²	1	1	yes	characteristic
44	C₉	—	3	1	no	—
45	C₉	—	6	1	no	—
46	C₂×C₃	—	9	1	no	—
47	C₂×C₃	—	27	1	no	—
48	C₂×C₃	—	27	1	no	—
49	D₃	—	3	1	no	—
50	D₃	—	9	1	no	—
51	D₃	—	9	1	no	—
52	D₃	—	9	1	no	—
53	D₃	—	9	1	no	—
54	D₃	—	9	1	no	—
55	D₃	—	18	1	no	—
56	D₃	—	18	1	no	—
57	C₂²	—	81	1	no	Sylow
58	C₃	—	2	1	no	—
59	C₃	—	3	1	no	—
60	C₃	—	6	1	no	—
61	C₃	D₃×D₉	1	1	yes	characteristic
62	C₃	((C₃⋊D₃)⋊C₃)⋊C₂	1	1	yes	characteristic
63	C₂	—	9	1	no	—
64	C₂	—	27	1	no	—
65	C₂	—	27	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²⋊C₉	C₂²
Frattini, socle	C₃²	D₃²
LCS	G ▷ C₃²⋊C₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #4181	C₂	semidirect
2. #4169	C₂	semidirect
3. (C₃⋊D₃)⋊C₉	C₂	semidirect
6. C₃²⋊C₉	C₂²	semidirect
10. C₃⋊D₉	D₃	semidirect
20. C₃×C₉	C₂×D₃	semidirect
23. C₃⋊D₃	D₉	semidirect
42. C₃²	C₂×D₉	semidirect

Maximal subgroups

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

subgroup	index
#4181	2
#4169	2
(C₃⋊D₃)⋊C₉	2
#1113	3
D₃×D₉	3

Subgroups — ((C3⋊D3)⋊C9)⋊C2 #66345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ((C₃⋊D₃)⋊C₉)⋊C₂ #66345