Subgroups — #131⋊C₉ #63429

Order 288.

37 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×#131	C₃	1	1	yes	maximal, characteristic
3	Q₈⋊C₉	C₄	1	1	yes	characteristic
4	C₈×C₉	—	4	1	no	maximal
5	C₃×#41	C₂×C₃	1	1	yes	characteristic
6	C₃×M₁₆	—	3	1	no	—
7	C₂×C₃×C₈	—	3	1	no	—
8	C₄×C₉	—	4	1	no	—
9	#131	C₉	1	1	yes	characteristic, complemented, Sylow
10	C₃×Q₈	C₃×C₄	1	1	yes	characteristic
11	C₃×D₄	—	3	1	no	—
12	C₂×C₃×C₄	—	3	1	no	—
13	C₃×C₈	—	3	1	no	—
14	C₃×C₈	A₄	1	1	yes	characteristic
15	C₂×C₉	—	4	1	no	—
16	#41	C₂×C₉	1	1	yes	characteristic
17	M₁₆	—	3	1	no	—
18	C₂×C₈	—	3	1	no	—
19	C₂²×C₃	—	3	1	no	—
20	C₃×C₄	—	3	1	no	—
21	C₃×C₄	C₂×A₄	1	1	yes	characteristic
22	C₉	—	4	1	no	Sylow
23	Q₈	C₄×C₉	1	1	yes	characteristic
24	D₄	—	3	1	no	—
25	C₂×C₄	—	3	1	no	—
26	C₈	—	3	1	no	—
27	C₈	C₂²⋊C₉	1	1	yes	characteristic
28	C₂×C₃	—	6	1	no	—
29	C₂×C₃	C₄×A₄	1	1	yes	characteristic
30	C₂²	—	3	1	no	—
31	C₄	—	3	1	no	—
32	C₄	C₂×C₂²⋊C₉	1	1	yes	characteristic
33	C₃	#131⋊C₃	1	1	yes	characteristic
34	C₂	—	6	1	no	—
35	C₂	C₄×C₂²⋊C₉	1	1	yes	characteristic

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

N	H ≅ G/N	type
9. #131	C₉	semidirect

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