Subgroups — #14558458

Order 2368.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924606	C₂	1	1	yes	maximal, characteristic
2	#11924604	C₂	1	1	yes	maximal, characteristic
3	#11924475	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#3866	—	2	1	no	—
5	#10596953	—	2	1	no	—
6	C₈×D₃₇	C₂²	1	1	yes	characteristic
7	C₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
8	#10596925	C₄	1	1	yes	characteristic, complemented
9	C₂×#3866	—	4	1	no	—
10	C₄×D₃₇	D₄	1	1	yes	characteristic
11	#64438	—	4	1	no	—
12	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
13	#64436	Q₈	1	1	yes	characteristic
14	C₂×D₃₇	SD₁₆	1	1	yes	characteristic
15	#3866	—	8	1	no	—
16	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
17	Dic₃₇	SD₁₆	1	1	yes	characteristic
18	C₂×C₃₇	#106	1	1	yes	characteristic
19	D₃₇	—	2	1	no	—
20	#365	—	37	1	no	maximal, Sylow
21	C₃₇	#365	1	1	yes	characteristic, complemented, Sylow
22	M₃₂	—	37	1	no	—
23	#108	—	37	1	no	—
24	#106	—	37	1	no	—
25	M₁₆	—	74	1	no	—
26	C₂×C₈	—	37	1	no	—
27	C₄⋊C₄	—	74	1	no	—
28	C₁₆	—	37	1	no	—
29	C₁₆	#3866	1	1	yes	characteristic, complemented
30	C₂×C₄	—	37	1	no	—
31	C₂×C₄	—	148	1	no	—
32	C₈	—	37	1	no	—
33	C₈	—	148	1	no	—
34	C₈	C₂×#3866	1	1	yes	characteristic
35	C₂²	—	37	1	no	—
36	C₄	—	37	1	no	—
37	C₄	—	296	1	no	—
38	C₄	C₄⋊#3866	1	1	yes	characteristic
39	C₂	—	74	1	no	—
40	C₂	#11924604	1	1	yes	characteristic

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

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