Subgroups — #14558397

Order 2368.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#64438	C₂	1	2	yes	maximal
2	C₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#64438	—	2	2	no	—
4	C₂×C₈×C₃₇	C₄	1	1	yes	characteristic
5	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
6	C₂×#64436	C₄	1	1	yes	characteristic
7	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₃₇	D₄	1	1	yes	characteristic
9	C₂×Dic₃₇	Q₈	1	1	yes	characteristic
10	#64438	—	4	2	no	—
11	C₈×C₃₇	—	2	1	no	—
12	#64436	C₈	1	2	yes	complemented
13	C₂²×C₃₇	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
15	C₄×C₃₇	M₁₆	1	1	yes	characteristic
16	Dic₃₇	—	2	1	no	—
17	Dic₃₇	D₈	1	1	yes	characteristic
18	Dic₃₇	Q₁₆	1	1	yes	characteristic
19	C₂×C₃₇	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₃₇	#107	1	1	yes	characteristic
21	C₂×C₃₇	#108	1	1	yes	characteristic
22	#335	—	37	1	no	maximal, Sylow
23	C₃₇	#335	1	1	yes	characteristic, complemented, Sylow
24	C₄⋊C₈	—	37	2	no	—
25	C₄×C₈	—	37	1	no	—
26	C₂×C₈	—	37	1	no	—
27	C₂×C₈	—	74	2	no	—
28	C₂×C₈	#3866	1	1	yes	characteristic
29	C₄²	—	37	1	no	—
30	C₂×C₄	—	37	1	no	—
31	C₂×C₄	—	37	1	no	—
32	C₂×C₄	C₂×#3866	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	37	2	no	—
35	C₈	—	148	2	no	—
36	C₂²	C₄⋊#3866	1	1	yes	characteristic
37	C₄	—	37	1	no	—
38	C₄	—	37	1	no	—
39	C₄	—	74	1	no	—
40	C₄	D₃₇⋊C₈	1	1	yes	characteristic
41	C₄	#10596957	1	1	yes	characteristic
42	C₂	#11924603	1	1	yes	characteristic
43	C₂	#11924605	1	1	yes	characteristic
44	C₂	#11924606	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. #64436	C₈	semidirect
23. C₃₇	#335	semidirect

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