Subgroups — #14557357

Order 2368.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924476	C₂	1	1	yes	maximal, characteristic
2	#11924468	C₂	1	1	yes	maximal, characteristic
3	#108×C₃₇	C₂	1	1	yes	maximal, characteristic
4	M₁₆×C₃₇	—	2	1	no	—
5	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₃₇	—	2	1	no	—
7	#10596925	C₄	1	2	yes	complemented
8	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
9	C₂×Dic₃₇	—	4	1	no	—
10	C₈×C₃₇	—	4	1	no	—
11	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₇	Q₈	1	1	yes	characteristic
13	C₂²×C₃₇	SD₁₆	1	1	yes	characteristic
14	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₃₇	SD₁₆	1	1	yes	characteristic
16	Dic₃₇	—	8	1	no	—
17	C₂×C₃₇	—	2	1	no	—
18	C₂×C₃₇	#106	1	1	yes	characteristic
19	#365	—	37	1	no	maximal, Sylow
20	C₃₇	#365	1	1	yes	characteristic, complemented, Sylow
21	M₃₂	—	37	1	no	—
22	#108	D₃₇	1	1	yes	characteristic
23	#106	—	37	1	no	—
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
26	C₄⋊C₄	—	74	1	no	—
27	C₁₆	—	37	2	no	—
28	C₂×C₄	—	148	1	no	—
29	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
30	C₈	—	4	1	no	—
31	C₈	Dic₇₄	1	1	yes	characteristic
32	C₈	C₄×D₃₇	1	1	yes	characteristic
33	C₂²	#10596941	1	1	yes	characteristic
34	C₄	—	296	1	no	—
35	C₄	#10596936	1	1	yes	characteristic
36	C₄	#10596940	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#11924467	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. #10596925	C₄	semidirect
20. C₃₇	#365	semidirect

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