Subgroups — #14558393

Order 2368.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924603	C₂	1	2	yes	maximal
2	#11924534	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×C₃₇	C₄	1	1	yes	characteristic
4	C₂×Dic₇₄	C₄	1	1	yes	characteristic
5	C₂×#64438	—	2	2	no	—
6	#10596936	—	2	2	no	—
7	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
8	Q₈×C₃₇	—	4	1	no	—
9	C₂×C₄×C₃₇	—	2	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	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₃₇	—	2	1	no	—
17	C₄×C₃₇	—	4	1	no	—
18	Dic₃₇	—	4	1	no	—
19	Dic₃₇	SD₁₆	1	2	yes	—
20	Dic₃₇	Q₁₆	1	2	yes	—
21	C₂×C₃₇	#100	1	1	yes	characteristic
22	C₂×C₃₇	#103	1	2	yes	—
23	#333	—	37	1	no	maximal, Sylow
24	C₃₇	#333	1	1	yes	characteristic, complemented, Sylow
25	C₄⋊Q₈	—	37	1	no	—
26	C₄⋊C₈	—	37	2	no	—
27	C₂×Q₈	—	37	1	no	—
28	C₂×Q₈	#3866	1	1	yes	characteristic
29	C₂×C₈	—	74	2	no	—
30	C₄⋊C₄	—	74	2	no	—
31	C₄²	—	37	1	no	—
32	Q₈	—	4	1	no	—
33	Q₈	—	148	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	37	2	no	—
36	C₂×C₄	—	74	1	no	—
37	C₂×C₄	C₂×#3866	1	1	yes	characteristic
38	C₈	—	148	2	no	—
39	C₂²	C₂²⋊#3866	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	—	4	1	no	—
42	C₄	—	37	2	no	—
43	C₄	—	37	2	no	—
44	C₄	—	148	1	no	—
45	C₂	#11924596	1	1	yes	characteristic
46	C₂	#11924599	1	2	yes	—

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

N	H ≅ G/N	type
24. C₃₇	#333	semidirect

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