Subgroups — #41⋊C₉ #3693

Order 144.

25 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#41	C₃	1	1	yes	maximal, characteristic
3	C₄×C₉	—	4	1	no	maximal
4	C₃×Q₈	C₂×C₃	1	1	yes	characteristic
5	C₃×D₄	—	3	1	no	—
6	C₂×C₃×C₄	—	3	1	no	—
7	C₂×C₉	—	4	1	no	—
8	#41	C₉	1	1	yes	characteristic, complemented, Sylow
9	C₂²×C₃	—	3	1	no	—
10	C₃×C₄	—	3	1	no	—
11	C₃×C₄	A₄	1	1	yes	characteristic
12	C₉	—	4	1	no	Sylow
13	Q₈	C₂×C₉	1	1	yes	characteristic
14	D₄	—	3	1	no	—
15	C₂×C₄	—	3	1	no	—
16	C₂×C₃	—	6	1	no	—
17	C₂×C₃	C₂×A₄	1	1	yes	characteristic
18	C₂²	—	3	1	no	—
19	C₄	—	3	1	no	—
20	C₄	C₂²⋊C₉	1	1	yes	characteristic
21	C₃	#41⋊C₃	1	1	yes	characteristic
22	C₂	—	6	1	no	—
23	C₂	C₂×C₂²⋊C₉	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. Q₈⋊C₉	C₂	semidirect
8. #41	C₉	semidirect

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