Subgroups — #37564306

Order 24224.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27131072	C₂	1	2	yes	maximal
2	C₂×Q₈×C₇₅₇	C₂	1	1	yes	maximal, characteristic
3	#20258493	—	2	2	no	—
4	Q₈×C₇₅₇	—	2	2	no	—
5	C₂×C₄×C₇₅₇	C₄	1	2	yes	—
6	C₂×C₄×C₇₅₇	C₂²	1	1	yes	characteristic
7	C₂²×C₇₅₇	C₂×C₄	1	1	yes	characteristic
8	C₄×C₇₅₇	—	2	2	no	—
9	C₄×C₇₅₇	D₄	1	2	yes	—
10	C₂×C₇₅₇	—	2	1	no	—
11	C₂×C₇₅₇	C₂²⋊C₄	1	1	yes	characteristic
12	C₇₅₇	#101	1	1	yes	characteristic, complemented, Sylow
13	#101	—	757	1	no	maximal, Sylow
14	C₂×Q₈	D₇₅₇	1	1	yes	characteristic
15	M₁₆	—	757	2	no	—
16	Q₈	—	2	2	no	—
17	C₂×C₄	Dic₇₅₇	1	2	yes	—
18	C₂×C₄	C₂×D₇₅₇	1	1	yes	characteristic
19	C₈	—	1514	2	no	—
20	C₂²	C₂×Dic₇₅₇	1	1	yes	characteristic
21	C₄	—	2	2	no	—
22	C₄	C₂²⋊D₇₅₇	1	2	yes	—
23	C₂	—	2	1	no	—
24	C₂	C₂²⋊Dic₇₅₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₇₅₇	#101	semidirect

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