Subgroups — #63391

Order 288.

69 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	#3667	C₂	1	2	yes	maximal, complemented
3	#833	—	3	1	no	maximal
4	C₂³×C₉	C₄	1	2	yes	—
5	D₄×C₉	—	2	2	no	—
6	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₉⋊C₈	—	2	2	no	—
8	C₂×C₃×D₄	D₃	1	1	yes	characteristic
9	#208	—	3	2	no	—
10	C₂²×C₉	—	2	2	no	—
11	C₂²×C₉	—	4	2	no	—
12	C₂²×C₉	C₂×C₄	1	1	yes	characteristic
13	C₄×C₉	D₄	1	2	yes	—
14	#100	—	9	1	no	Sylow
15	C₂³×C₃	Dic₃	1	2	yes	—
16	C₃×D₄	—	2	2	no	—
17	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
18	C₃⋊C₈	—	6	2	no	—
19	C₂×C₉	—	2	1	no	—
20	C₂×C₉	—	4	2	no	—
21	C₂×C₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×D₄	D₉	1	1	yes	characteristic
23	M₁₆	—	9	2	no	—
24	C₂²×C₃	—	2	2	no	—
25	C₂²×C₃	—	4	2	no	—
26	C₂²×C₃	C₂×Dic₃	1	1	yes	characteristic
27	C₃×C₄	#67	1	2	yes	—
28	C₉	#100	1	1	yes	characteristic, complemented, Sylow
29	C₂³	Dic₉	1	2	yes	—
30	D₄	—	2	2	no	—
31	C₂×C₄	C₂×D₉	1	1	yes	characteristic
32	C₈	—	18	2	no	—
33	C₂×C₃	—	2	1	no	—
34	C₂×C₃	—	4	2	no	—
35	C₂×C₃	#217	1	1	yes	characteristic
36	C₂²	—	2	2	no	—
37	C₂²	—	4	2	no	—
38	C₂²	C₂×Dic₉	1	1	yes	characteristic
39	C₄	#611	1	2	yes	—
40	C₃	#833	1	1	yes	characteristic
41	C₂	—	2	1	no	—
42	C₂	—	4	2	no	—
43	C₂	#3676	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #3667	C₂	semidirect
28. C₉	#100	semidirect

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