Subgroups — #63788

Order 288.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#638	C₂	1	1	yes	maximal, characteristic
2	#3792	C₂	1	2	yes	maximal, complemented
3	C₂³×C₃²	C₄	1	1	yes	characteristic
4	C₂²×C₃⋊D₃	C₄	1	1	yes	characteristic
5	#638	—	2	2	no	—
6	C₂×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
7	#622	—	2	2	no	—
8	C₂×#67	—	6	2	no	—
9	C₂²×C₃²	—	2	1	no	—
10	C₂²×C₃²	—	4	1	no	—
11	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃⋊D₃	—	2	1	no	—
13	C₂×C₃⋊D₃	—	4	1	no	—
14	C₃⋊Dic₃	D₄	1	2	yes	—
15	#100	—	9	1	no	maximal, Sylow
16	C₂³×C₃	—	2	2	no	—
17	C₂²×D₃	—	6	2	no	—
18	#67	—	6	8	no	—
19	C₂×Dic₃	—	6	2	no	—
20	C₂×C₃²	—	2	1	no	—
21	C₂×C₃²	—	4	1	no	—
22	C₂×C₃²	C₂²⋊C₄	1	1	yes	characteristic
23	C₃⋊D₃	—	4	1	no	—
24	C₂×D₄	—	9	1	no	—
25	M₁₆	—	9	2	no	—
26	C₂²×C₃	—	2	4	no	—
27	C₂²×C₃	—	2	2	no	—
28	C₂²×C₃	—	4	4	no	—
29	C₂×D₃	—	6	4	no	—
30	C₂×D₃	—	12	4	no	—
31	Dic₃	—	6	4	no	—
32	C₃²	#100	1	1	yes	characteristic, complemented, Sylow
33	C₂³	—	9	1	no	—
34	C₂³	#157	1	1	yes	characteristic
35	D₄	—	18	2	no	—
36	C₂×C₄	—	9	1	no	—
37	C₈	—	18	2	no	—
38	C₂×C₃	—	2	4	no	—
39	C₂×C₃	—	2	2	no	—
40	C₂×C₃	—	4	4	no	—
41	D₃	—	12	4	no	—
42	C₂²	—	2	1	no	—
43	C₂²	—	4	1	no	—
44	C₂²	—	18	1	no	—
45	C₂²	—	36	1	no	—
46	C₂²	C₂×#157	1	1	yes	characteristic
47	C₄	—	9	2	no	—
48	C₃	—	2	2	no	—
49	C₂	—	2	1	no	—
50	C₂	—	4	1	no	—
51	C₂	—	36	1	no	—
52	C₂	C₂²⋊#157	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #3792	C₂	semidirect
32. C₃²	#100	semidirect

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