Subgroups — #38737913

Order 25184.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₁₄₈	C₂	1	1	yes	maximal, characteristic
2	C₇₈₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×C₇₈₇	C₂	1	1	yes	maximal, characteristic
4	Dic₁₅₇₄	—	2	1	no	—
5	Q₈×C₇₈₇	—	2	1	no	—
6	C₈×C₇₈₇	C₂²	1	1	yes	characteristic
7	C₄×C₇₈₇	—	4	1	no	—
8	C₄×C₇₈₇	D₄	1	1	yes	characteristic
9	Dic₇₈₇	—	4	1	no	—
10	C₂×C₇₈₇	D₈	1	1	yes	characteristic
11	C₇₈₇	Q₃₂	1	1	yes	characteristic, complemented, Sylow
12	Q₃₂	—	787	1	no	maximal, Sylow
13	Q₁₆	—	787	1	no	—
14	Q₁₆	D₇₈₇	1	1	yes	characteristic
15	C₁₆	—	787	1	no	—
16	Q₈	—	2	1	no	—
17	Q₈	—	1574	1	no	—
18	C₈	C₂×D₇₈₇	1	1	yes	characteristic
19	C₄	—	4	1	no	—
20	C₄	—	3148	1	no	—
21	C₄	C₂²⋊D₇₈₇	1	1	yes	characteristic
22	C₂	#27160461	1	1	yes	characteristic

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

N	H ≅ G/N	type
11. C₇₈₇	Q₃₂	semidirect

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