Subgroups — #37562373

Order 24032.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26046626	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇₅₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	M₁₆×C₇₅₁	C₂	1	1	yes	maximal, characteristic
4	C₇₅₁⋊C₈	—	2	1	no	—
5	C₇₅₁⋊C₈	C₄	1	2	yes	—
6	C₂×C₄×C₇₅₁	C₂²	1	1	yes	characteristic
7	C₈×C₇₅₁	—	2	1	no	—
8	C₂²×C₇₅₁	Q₈	1	1	yes	characteristic
9	C₄×C₇₅₁	C₂×C₄	1	1	yes	characteristic
10	C₄×C₇₅₁	D₄	1	1	yes	characteristic
11	C₂×C₇₅₁	—	2	1	no	—
12	C₂×C₇₅₁	C₄⋊C₄	1	1	yes	characteristic
13	C₇₅₁	#108	1	1	yes	characteristic, complemented, Sylow
14	#108	—	751	1	no	maximal, Sylow
15	M₁₆	—	751	1	no	—
16	M₁₆	D₇₅₁	1	1	yes	characteristic
17	C₂×C₈	—	751	1	no	—
18	C₂×C₄	C₂×D₇₅₁	1	1	yes	characteristic
19	C₈	—	2	1	no	—
20	C₈	—	1502	1	no	—
21	C₈	—	751	2	no	—
22	C₂²	Dic₁₅₀₂	1	1	yes	characteristic
23	C₄	C₄×D₇₅₁	1	1	yes	characteristic
24	C₄	C₂²⋊D₇₅₁	1	1	yes	characteristic
25	C₂	—	2	1	no	—
26	C₂	Dic₇₅₁⋊C₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. C₇₅₁	#108	semidirect

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