Subgroups — #17992811

Order 4736.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅₉₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#14557252	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×D₃₂	C₂	1	1	yes	maximal, characteristic
4	Dic₂₉₆	—	2	1	no	—
5	D₁₆×C₃₇	—	2	1	no	—
6	C₃₂×C₃₇	C₂²	1	1	yes	characteristic
7	D₈×C₃₇	—	4	1	no	—
8	Dic₁₄₈	—	4	1	no	—
9	C₁₆×C₃₇	D₄	1	1	yes	characteristic
10	D₄×C₃₇	—	8	1	no	—
11	Dic₇₄	—	8	1	no	—
12	C₈×C₃₇	D₈	1	1	yes	characteristic
13	C₂²×C₃₇	—	16	1	no	—
14	C₄×C₃₇	D₁₆	1	1	yes	characteristic
15	Dic₃₇	—	16	1	no	—
16	SD₁₂₈	—	37	1	no	maximal, Sylow
17	C₂×C₃₇	—	32	1	no	—
18	C₂×C₃₇	D₃₂	1	1	yes	characteristic
19	Q₆₄	—	37	1	no	—
20	D₃₂	D₃₇	1	1	yes	characteristic
21	C₆₄	—	37	1	no	—
22	C₃₇	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
23	Q₃₂	—	74	1	no	—
24	D₁₆	—	2	1	no	—
25	C₃₂	C₂×D₃₇	1	1	yes	characteristic
26	Q₁₆	—	148	1	no	—
27	D₈	—	4	1	no	—
28	C₁₆	C₂²⋊D₃₇	1	1	yes	characteristic
29	Q₈	—	296	1	no	—
30	D₄	—	8	1	no	—
31	C₈	#10596939	1	1	yes	characteristic
32	C₂²	—	16	1	no	—
33	C₄	—	592	1	no	—
34	C₄	#11924477	1	1	yes	characteristic
35	C₂	—	32	1	no	—
36	C₂	#14557368	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.