Subgroups — #14557359

Order 2368.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924470	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
4	C₄⋊Dic₃₇	—	2	2	no	—
5	C₁₆×C₃₇	C₄	1	2	yes	complemented
6	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
7	C₂×Dic₃₇	—	4	2	no	—
8	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₃₇	Q₈	1	1	yes	characteristic
10	C₂²×C₃₇	D₈	1	1	yes	characteristic
11	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₃₇	Q₁₆	1	1	yes	characteristic
13	Dic₃₇	—	8	2	no	—
14	C₂×C₃₇	#107	1	1	yes	characteristic
15	C₂×C₃₇	D₁₆	1	1	yes	characteristic
16	C₂×C₃₇	Q₃₂	1	1	yes	characteristic
17	#366	—	37	1	no	maximal, Sylow
18	C₃₇	#366	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₁₆	D₃₇	1	1	yes	characteristic
20	#107	—	37	2	no	—
21	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
22	C₄⋊C₄	—	74	2	no	—
23	C₁₆	Dic₃₇	1	2	yes	complemented
24	C₂×C₄	—	148	2	no	—
25	C₂×C₄	D₁₄₈	1	1	yes	characteristic
26	C₈	Dic₇₄	1	1	yes	characteristic
27	C₈	C₂×Dic₃₇	1	1	yes	characteristic
28	C₂²	D₂₉₆	1	1	yes	characteristic
29	C₄	—	296	2	no	—
30	C₄	Dic₁₄₈	1	1	yes	characteristic
31	C₄	C₄⋊Dic₃₇	1	1	yes	characteristic
32	C₂	#11924470	1	1	yes	characteristic
33	C₂	D₅₉₂	1	1	yes	characteristic
34	C₂	Dic₂₉₆	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.