Subgroups — #11757331

Order 972.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#6867	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊Dic₉	—	3	1	no	maximal
3	#66316	—	3	3	no	maximal
4	#6867	C₄	1	1	yes	characteristic, complemented, Sylow
5	C₂×C₃²×C₉	D₃	1	1	yes	characteristic
6	C₂×C₃²⋊C₉	D₃	1	3	yes	—
7	C₃×C₃⋊Dic₃	—	9	1	no	—
8	C₃⋊Dic₉	—	3	1	no	—
9	C₃⋊Dic₉	—	3	3	no	—
10	C₃×Dic₉	—	9	3	no	—
11	C₃²×C₉	Dic₃	1	1	yes	characteristic
12	C₃²⋊C₉	Dic₃	1	3	yes	—
13	C₂×C₃³	C₃⋊D₃	1	1	yes	characteristic
14	C₂×C₃×C₉	—	3	1	no	—
15	C₂×C₃×C₉	—	3	3	no	—
16	C₂×C₃×C₉	—	6	1	no	—
17	C₂×C₃×C₉	D₉	1	3	yes	—
18	C₃⋊Dic₃	—	9	1	no	—
19	C₃×Dic₃	—	27	3	no	—
20	C₃×Dic₃	—	27	1	no	—
21	Dic₉	—	9	3	no	—
22	Dic₉	—	27	3	no	—
23	C₃³	C₃⋊Dic₃	1	1	yes	characteristic
24	C₃×C₉	—	3	1	no	—
25	C₃×C₉	—	3	3	no	—
26	C₃×C₉	—	6	1	no	—
27	C₃×C₉	Dic₉	1	3	yes	complemented
28	C₂×C₃²	—	2	1	no	—
29	C₂×C₃²	—	3	3	no	—
30	C₂×C₃²	C₃⋊D₉	1	1	yes	characteristic
31	C₂×C₃²	#272	1	1	yes	characteristic
32	C₂×C₉	—	3	3	no	—
33	C₂×C₉	—	9	3	no	—
34	C₃×C₄	—	81	1	no	—
35	Dic₃	—	27	1	no	—
36	Dic₃	—	27	3	no	—
37	C₃²	—	2	1	no	—
38	C₃²	—	3	3	no	—
39	C₃²	C₃⋊Dic₉	1	1	yes	characteristic
40	C₃²	#1084	1	1	yes	characteristic
41	C₉	—	3	3	no	—
42	C₉	—	9	3	no	—
43	C₂×C₃	—	3	1	no	—
44	C₂×C₃	—	6	1	no	—
45	C₂×C₃	#4181	1	1	yes	characteristic
46	C₂×C₃	#4184	1	3	yes	—
47	C₄	—	81	1	no	Sylow
48	C₃	—	3	1	no	—
49	C₃	—	6	1	no	—
50	C₃	#66328	1	1	yes	characteristic
51	C₃	#66331	1	3	yes	—
52	C₂	#92208	1	1	yes	characteristic

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

N	H ≅ G/N	type
4. #6867	C₄	semidirect
27. C₃×C₉	Dic₉	semidirect

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