Subgroups — C₉×#564⋊C₃ #13152251

Order 1728.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

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