Subgroups — #11757430

Order 972.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₉⋊(C₂²⋊C₉)	C₃	1	1	yes	maximal, characteristic
3	#66353	C₃	1	1	yes	maximal, characteristic
4	#66353	C₃	1	1	yes	maximal, characteristic
5	#6875	—	4	1	no	maximal, Sylow
6	C₂×C₂₇⋊C₃	—	3	1	no	—
7	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
8	C₃×C₂²⋊C₉	—	3	1	no	—
9	C₂²×C₂₇	—	3	1	no	—
10	C₂²⋊C₂₇	—	3	1	no	—
11	C₂²⋊C₂₇	C₉	1	3	yes	complemented
12	C₂₇⋊C₃	—	4	1	no	—
13	C₂₇⋊C₃	—	4	1	no	—
14	C₂₇⋊C₃	A₄	1	1	yes	characteristic
15	C₉⋊C₉	—	4	1	no	—
16	C₂×C₃×C₉	—	3	1	no	—
17	C₂×C₂₇	—	3	3	no	—
18	C₂²×C₃²	3₋¹⁺²	1	1	yes	characteristic
19	C₂²×C₉	C₃×C₉	1	1	yes	characteristic
20	C₂²×C₉	3₋¹⁺²	1	1	yes	characteristic
21	C₂²×C₉	3₋¹⁺²	1	1	yes	characteristic
22	C₂²⋊C₉	—	9	1	no	—
23	C₃×C₉	—	12	1	no	—
24	C₃×C₉	C₃×A₄	1	1	yes	characteristic
25	C₂₇	—	3	1	no	—
26	C₂₇	—	4	3	no	—
27	C₂₇	—	12	1	no	—
28	C₂×C₃²	—	3	1	no	—
29	C₂×C₉	—	3	1	no	—
30	C₂×C₉	—	3	1	no	—
31	C₂×C₉	—	3	1	no	—
32	C₂²×C₃	—	3	1	no	—
33	C₂²×C₃	C₉⋊C₉	1	1	yes	characteristic
34	C₃²	C₉⋊A₄	1	1	yes	characteristic
35	C₉	—	36	1	no	—
36	C₉	C₉×A₄	1	1	yes	characteristic
37	C₉	C₉⋊A₄	1	1	yes	characteristic
38	C₉	#1094	1	1	yes	characteristic
39	C₂×C₃	—	3	1	no	—
40	C₂×C₃	—	9	1	no	—
41	C₂²	#6875	1	1	yes	characteristic, complemented, Sylow
42	C₃	—	3	1	no	—
43	C₃	(C₂²⋊C₉)⋊C₉	1	1	yes	characteristic
44	C₂	—	3	1	no	—

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

N	H ≅ G/N	type
11. C₂²⋊C₂₇	C₉	semidirect
41. C₂²	#6875	semidirect

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