Subgroups — #37564304

Order 24224.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27131072	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×C₇₅₇	C₂	1	1	yes	maximal, characteristic
3	#20258493	—	2	2	no	—
4	C₂³×C₇₅₇	C₄	1	2	yes	—
5	D₄×C₇₅₇	—	2	2	no	—
6	C₂×C₄×C₇₅₇	C₂²	1	1	yes	characteristic
7	C₂²×C₇₅₇	—	2	2	no	—
8	C₂²×C₇₅₇	—	4	2	no	—
9	C₂²×C₇₅₇	C₂×C₄	1	1	yes	characteristic
10	C₄×C₇₅₇	D₄	1	2	yes	—
11	C₂×C₇₅₇	—	2	1	no	—
12	C₂×C₇₅₇	—	4	2	no	—
13	C₂×C₇₅₇	C₂²⋊C₄	1	1	yes	characteristic
14	C₇₅₇	#100	1	1	yes	characteristic, complemented, Sylow
15	#100	—	757	1	no	maximal, Sylow
16	C₂×D₄	D₇₅₇	1	1	yes	characteristic
17	M₁₆	—	757	2	no	—
18	C₂³	Dic₇₅₇	1	2	yes	—
19	D₄	—	2	2	no	—
20	C₂×C₄	C₂×D₇₅₇	1	1	yes	characteristic
21	C₈	—	1514	2	no	—
22	C₂²	—	2	2	no	—
23	C₂²	—	4	2	no	—
24	C₂²	C₂×Dic₇₅₇	1	1	yes	characteristic
25	C₄	C₂²⋊D₇₅₇	1	2	yes	—
26	C₂	—	2	1	no	—
27	C₂	—	4	2	no	—
28	C₂	C₂²⋊Dic₇₅₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #27131072	C₂	semidirect
14. C₇₅₇	#100	semidirect

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