Subgroups — #14558444

Order 2368.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924597	C₂	1	2	yes	maximal
2	#11924536	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₇₄	C₄	1	1	yes	characteristic
4	C₂×Dic₇₄	C₂²	1	1	yes	characteristic
5	#10596957	—	2	2	no	—
6	C₄²×C₃₇	C₄	1	1	yes	characteristic
7	C₄⋊Dic₃₇	—	2	2	no	—
8	C₂×C₄×C₃₇	—	2	1	no	—
9	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₃₇	—	2	1	no	—
11	C₂×Dic₃₇	D₄	1	2	yes	—
12	Dic₇₄	—	4	1	no	—
13	Dic₇₄	—	4	1	no	—
14	#64438	—	4	2	no	—
15	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₃₇	—	2	2	no	—
17	C₄×C₃₇	—	2	1	no	—
18	Dic₃₇	—	2	2	no	—
19	Dic₃₇	—	4	1	no	—
20	C₂×C₃₇	—	2	1	no	—
21	C₂×C₃₇	#99	1	1	yes	characteristic
22	#356	—	37	1	no	maximal, Sylow
23	C₃₇	#356	1	1	yes	characteristic, complemented, Sylow
24	C₄⋊Q₈	—	37	1	no	—
25	#101	—	37	2	no	—
26	C₂×Q₈	—	37	1	no	—
27	C₂×Q₈	—	37	1	no	—
28	M₁₆	—	74	2	no	—
29	C₄⋊C₄	—	74	2	no	—
30	C₄²	#3866	1	1	yes	characteristic
31	Q₈	—	148	1	no	—
32	Q₈	—	148	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	37	2	no	—
35	C₂×C₄	—	74	1	no	—
36	C₂×C₄	C₂×#3866	1	1	yes	characteristic
37	C₈	—	148	2	no	—
38	C₂²	C₂²⋊#3866	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	2	1	no	—
41	C₄	—	74	2	no	—
42	C₄	—	148	1	no	—
43	C₂	—	2	1	no	—
44	C₂	#11924595	1	1	yes	characteristic

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

N	H ≅ G/N	type
23. C₃₇	#356	semidirect

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