Subgroups — #14558430

Order 2368.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924610	C₂	1	2	yes	maximal, complemented
2	C₂×#10596929	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₃₇	C₄	1	1	yes	characteristic
4	C₂×C₈×C₃₇	C₄	1	1	yes	characteristic
5	C₂×#64436	C₂²	1	1	yes	characteristic
6	#10596929	—	2	2	no	—
7	#10596927	—	2	2	no	—
8	C₂²×D₃₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₃₇	C₈	1	1	yes	characteristic
11	C₄×D₃₇	—	2	1	no	—
12	C₄×D₃₇	—	2	1	no	—
13	C₈×C₃₇	—	2	1	no	—
14	#64436	D₄	1	2	yes	—
15	C₂²×C₃₇	C₂×C₈	1	1	yes	characteristic
16	C₂×D₃₇	—	2	1	no	—
17	C₂×D₃₇	—	4	1	no	—
18	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₃₇	M₁₆	1	1	yes	characteristic
20	Dic₃₇	—	2	1	no	—
21	C₂×C₃₇	—	2	1	no	—
22	C₂×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
23	D₃₇	—	4	1	no	—
24	#349	—	37	1	no	maximal, Sylow
25	C₃₇	#349	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	37	1	no	—
27	M₃₂	—	37	2	no	—
28	C₂²×C₄	—	37	1	no	—
29	M₁₆	—	74	2	no	—
30	C₂×C₈	—	37	1	no	—
31	C₂×C₈	#3866	1	1	yes	characteristic
32	C₁₆	—	74	2	no	—
33	C₂³	—	37	1	no	—
34	C₂×C₄	—	37	1	no	—
35	C₂×C₄	—	74	1	no	—
36	C₂×C₄	—	74	1	no	—
37	C₂×C₄	C₂×#3866	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	—	37	2	no	—
40	C₂²	—	74	1	no	—
41	C₂²	—	148	1	no	—
42	C₂²	D₃₇⋊C₈	1	1	yes	characteristic
43	C₄	—	74	1	no	—
44	C₄	#10596953	1	1	yes	characteristic
45	C₄	C₂²⋊#3866	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	148	1	no	—
48	C₂	#11924593	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #11924610	C₂	semidirect
25. C₃₇	#349	semidirect

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