Subgroups — #14558441

Order 2368.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924597	C₂	1	2	yes	maximal, complemented
2	#11924523	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×C₃₇	C₄	1	1	yes	characteristic
4	C₂×Dic₇₄	C₂²	1	1	yes	characteristic
5	#10596957	—	2	2	no	—
6	C₂²⋊Dic₃₇	—	2	2	no	—
7	C₄×Dic₃₇	C₄	1	1	yes	characteristic
8	C₂³×C₃₇	—	2	1	no	—
9	D₄×C₃₇	—	4	1	no	—
10	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₃₇	—	2	1	no	—
12	C₂×Dic₃₇	D₄	1	2	yes	—
13	Dic₇₄	—	4	1	no	—
14	#64438	—	4	2	no	—
15	C₂²×C₃₇	—	4	2	no	—
16	C₂²×C₃₇	—	4	1	no	—
17	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₃₇	—	2	1	no	—
19	Dic₃₇	—	2	2	no	—
20	Dic₃₇	—	4	1	no	—
21	C₂×C₃₇	—	2	1	no	—
22	C₂×C₃₇	—	8	1	no	—
23	C₂×C₃₇	#99	1	1	yes	characteristic
24	#355	—	37	1	no	maximal, Sylow
25	C₃₇	#355	1	1	yes	characteristic, complemented, Sylow
26	#124	—	37	1	no	—
27	#101	—	37	2	no	—
28	C₂×Q₈	—	37	1	no	—
29	C₂×D₄	#3866	1	1	yes	characteristic
30	M₁₆	—	74	2	no	—
31	C₂²⋊C₄	—	74	2	no	—
32	C₄²	—	37	1	no	—
33	C₂³	—	2	1	no	—
34	Q₈	—	148	1	no	—
35	D₄	—	4	1	no	—
36	C₂×C₄	—	37	2	no	—
37	C₂×C₄	—	74	1	no	—
38	C₂×C₄	C₂×#3866	1	1	yes	characteristic
39	C₈	—	148	2	no	—
40	C₂²	—	4	2	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂²⋊#3866	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	74	2	no	—
45	C₄	—	148	1	no	—
46	C₂	—	2	1	no	—
47	C₂	—	8	1	no	—
48	C₂	#11924594	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #11924597	C₂	semidirect
25. C₃₇	#355	semidirect

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