Subgroups — #13152269

Order 1728.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#564	C₃	1	1	yes	maximal, characteristic
2	#564⋊C₉	C₃	1	3	yes	maximal, complemented
3	#88455	—	4	5	no	maximal
4	C₃²×#125	—	3	5	no	—
5	C₃×#564	—	3	1	no	—
6	C₃×#564	C₃²	1	1	yes	characteristic
7	C₃²×C₄⋊C₄	—	3	10	no	—
8	C₃²×C₄²	A₄	1	5	yes	—
9	C₄²⋊C₉	—	4	15	no	—
10	#1094	—	16	1	no	—
11	C₃×#125	—	3	15	no	—
12	C₃×#125	—	3	5	no	—
13	C₂×C₃²×C₄	—	3	5	no	—
14	#564	3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₄⋊C₄	—	3	30	no	—
16	C₃×C₄⋊C₄	—	3	10	no	—
17	C₃×C₄²	—	3	5	no	—
18	C₃×C₄²	C₃×A₄	1	5	yes	—
19	C₂²×C₃²	C₂²⋊A₄	1	1	yes	characteristic
20	C₃²×C₄	—	6	5	no	—
21	C₂²⋊C₉	—	16	3	no	—
22	#125	—	3	5	no	—
23	3₋¹⁺²	—	64	1	no	Sylow
24	C₂×C₃×C₄	—	3	15	no	—
25	C₂×C₃×C₄	—	3	5	no	—
26	C₂×C₃²	—	3	1	no	—
27	C₄⋊C₄	—	3	10	no	—
28	C₄²	#1094	1	5	yes	—
29	C₂²×C₃	—	3	1	no	—
30	C₂²×C₃	C₃×C₂²⋊A₄	1	1	yes	characteristic
31	C₃×C₄	—	6	15	no	—
32	C₃×C₄	—	6	5	no	—
33	C₃²	#564⋊C₃	1	1	yes	characteristic
34	C₉	—	64	3	no	—
35	C₂×C₄	—	3	5	no	—
36	C₂×C₃	—	3	3	no	—
37	C₂×C₃	—	3	1	no	—
38	C₂²	#88907	1	1	yes	characteristic
39	C₄	—	6	5	no	—
40	C₃	—	3	1	no	—
41	C₃	C₃×#564⋊C₃	1	1	yes	characteristic
42	C₂	—	3	1	no	—

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

N	H ≅ G/N	type
2. #564⋊C₉	C₃	semidirect
14. #564	3₋¹⁺²	semidirect

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