Subgroups — C₂³×Dic₇₅₇ #37564422

Order 24224.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₇₅₇	C₂	1	14	yes	maximal, direct product factor
2	C₂⁴×C₇₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₇₅₇	C₂²	1	28	yes	direct product factor
4	C₂³×C₇₅₇	C₄	1	8	yes	complemented
5	C₂³×C₇₅₇	C₂²	1	7	yes	—
6	C₂²×C₇₅₇	C₂×C₄	1	28	yes	complemented
7	C₂²×C₇₅₇	C₂³	1	7	yes	—
8	Dic₇₅₇	C₂³	1	8	yes	direct product factor
9	C₂×C₇₅₇	C₂²×C₄	1	14	yes	complemented
10	C₂×C₇₅₇	C₂⁴	1	1	yes	characteristic
11	C₇₅₇	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
12	C₂³×C₄	—	757	1	no	maximal, Sylow
13	C₂⁴	D₇₅₇	1	1	yes	characteristic
14	C₂²×C₄	—	757	14	no	—
15	C₂³	Dic₇₅₇	1	8	yes	direct product factor
16	C₂³	C₂×D₇₅₇	1	7	yes	—
17	C₂×C₄	—	757	28	no	—
18	C₂²	C₂×Dic₇₅₇	1	28	yes	direct product factor
19	C₂²	C₂²×D₇₅₇	1	7	yes	—
20	C₄	—	757	8	no	—
21	C₂	C₂²×Dic₇₅₇	1	14	yes	direct product factor
22	C₂	C₂³×D₇₅₇	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.