Subgroups — #35208331

Order 20704.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23780419	C₂	1	2	yes	maximal
2	C₂×Q₈×C₆₄₇	C₂	1	1	yes	maximal, characteristic
3	C₆₄₇⋊C₈	—	2	2	no	—
4	Q₈×C₆₄₇	—	2	2	no	—
5	C₂×C₄×C₆₄₇	C₄	1	2	yes	—
6	C₂×C₄×C₆₄₇	C₂²	1	1	yes	characteristic
7	C₂²×C₆₄₇	C₂×C₄	1	1	yes	characteristic
8	C₄×C₆₄₇	—	2	2	no	—
9	C₄×C₆₄₇	D₄	1	2	yes	—
10	C₂×C₆₄₇	—	2	1	no	—
11	C₂×C₆₄₇	C₂²⋊C₄	1	1	yes	characteristic
12	C₆₄₇	#101	1	1	yes	characteristic, complemented, Sylow
13	#101	—	647	1	no	maximal, Sylow
14	C₂×Q₈	D₆₄₇	1	1	yes	characteristic
15	M₁₆	—	647	2	no	—
16	Q₈	—	2	2	no	—
17	C₂×C₄	Dic₆₄₇	1	2	yes	—
18	C₂×C₄	C₂×D₆₄₇	1	1	yes	characteristic
19	C₈	—	1294	2	no	—
20	C₂²	C₂×Dic₆₄₇	1	1	yes	characteristic
21	C₄	—	2	2	no	—
22	C₄	C₂²⋊D₆₄₇	1	2	yes	—
23	C₂	—	2	1	no	—
24	C₂	C₂²⋊Dic₆₄₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₆₄₇	#101	semidirect

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