Subgroups — #63422

Order 288.

41 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	#837	—	3	1	no	maximal
3	Q₈⋊C₉	C₄	1	1	yes	characteristic, complemented
4	C₉⋊C₈	—	4	1	no	maximal
5	C₃×#41	D₃	1	1	yes	characteristic
6	C₄×Dic₃	—	3	1	no	—
7	#208	—	3	1	no	—
8	C₄×C₉	—	4	1	no	—
9	#104	—	9	1	no	Sylow
10	C₃×Q₈	Dic₃	1	1	yes	characteristic
11	C₃×D₄	—	3	1	no	—
12	C₂×C₃×C₄	—	3	1	no	—
13	C₂×Dic₃	—	6	1	no	—
14	C₃⋊C₈	—	6	1	no	—
15	C₂×C₉	—	4	1	no	—
16	#41	D₉	1	1	yes	characteristic
17	M₁₆	—	9	1	no	—
18	C₄²	—	9	1	no	—
19	C₂²×C₃	—	3	1	no	—
20	C₃×C₄	—	3	1	no	—
21	C₃×C₄	S₄	1	1	yes	characteristic
22	Dic₃	—	6	2	no	—
23	C₉	—	4	1	no	Sylow
24	Q₈	Dic₉	1	1	yes	characteristic
25	D₄	—	3	1	no	—
26	C₂×C₄	—	3	1	no	—
27	C₂×C₄	—	18	1	no	—
28	C₈	—	18	1	no	—
29	C₂×C₃	—	6	1	no	—
30	C₂×C₃	SL(2,ℤ/4)	1	1	yes	characteristic
31	C₂²	—	3	1	no	—
32	C₄	—	3	1	no	—
33	C₄	—	18	2	no	—
34	C₄	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic
35	C₃	GU(2,𝔽₃)	1	1	yes	characteristic
36	C₂	—	6	1	no	—
37	C₂	(C₂²⋊C₉)⋊C₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. Q₈⋊C₉	C₄	semidirect

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