Subgroups — #44526057

Order 30944.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29509155	C₂	1	2	yes	maximal
2	C₂×C₈×C₉₆₇	C₂	1	1	yes	maximal, characteristic
3	C₉₆₇⋊C₈	—	2	2	no	—
4	C₂×C₄×C₉₆₇	C₂²	1	1	yes	characteristic
5	C₈×C₉₆₇	C₄	1	2	yes	—
6	C₂²×C₉₆₇	Q₈	1	1	yes	characteristic
7	C₄×C₉₆₇	C₂×C₄	1	1	yes	characteristic
8	C₄×C₉₆₇	D₄	1	1	yes	characteristic
9	C₂×C₉₆₇	—	2	1	no	—
10	C₂×C₉₆₇	C₄⋊C₄	1	1	yes	characteristic
11	C₉₆₇	#108	1	1	yes	characteristic, complemented, Sylow
12	#108	—	967	1	no	maximal, Sylow
13	M₁₆	—	967	2	no	—
14	C₂×C₈	D₉₆₇	1	1	yes	characteristic
15	C₂×C₄	C₂×D₉₆₇	1	1	yes	characteristic
16	C₈	—	1934	2	no	—
17	C₈	Dic₉₆₇	1	2	yes	—
18	C₂²	Dic₁₉₃₄	1	1	yes	characteristic
19	C₄	C₂×Dic₉₆₇	1	1	yes	characteristic
20	C₄	D₃₈₆₈	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	C₄⋊Dic₉₆₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
11. C₉₆₇	#108	semidirect

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