Subgroups — C₉×S₄ #6252

Order 216.

37 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×S₄	C₃	1	1	yes	maximal, characteristic
3	D₄×C₉	—	3	1	no	maximal
4	D₃×C₉	—	4	1	no	maximal
5	C₃×A₄	C₂×C₃	1	1	yes	characteristic
6	C₂²×C₉	—	3	1	no	—
7	C₂²×C₉	D₃	1	1	yes	characteristic, complemented
8	C₂²⋊C₉	—	2	1	no	—
9	C₄×C₉	—	3	1	no	—
10	C₃×C₉	—	4	1	no	Sylow
11	S₄	C₉	1	1	yes	characteristic, direct product factor
12	C₃×D₄	—	3	1	no	—
13	C₃×D₃	—	4	1	no	—
14	C₂×C₉	—	3	1	no	—
15	C₂×C₉	—	6	1	no	—
16	C₂²×C₃	—	3	1	no	—
17	C₂²×C₃	C₃×D₃	1	1	yes	characteristic
18	A₄	—	2	1	no	—
19	A₄	C₂×C₉	1	1	yes	characteristic, complemented
20	C₃×C₄	—	3	1	no	—
21	C₃²	—	4	1	no	—
22	C₉	—	8	1	no	—
23	C₉	S₄	1	1	yes	characteristic, direct product factor
24	D₄	—	3	1	no	Sylow
25	C₂×C₃	—	3	1	no	—
26	C₂×C₃	—	6	1	no	—
27	D₃	—	4	1	no	—
28	C₂²	—	3	1	no	—
29	C₂²	D₃×C₉	1	1	yes	characteristic, complemented
30	C₄	—	3	1	no	—
31	C₃	—	4	1	no	—
32	C₃	—	8	1	no	—
33	C₃	C₃×S₄	1	1	yes	characteristic
34	C₂	—	3	1	no	—
35	C₂	—	6	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.