Subgroups — #37589969

Order 24608.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27134391	C₂	1	2	yes	maximal
2	C₈×D₇₆₉	C₂	1	1	yes	maximal, characteristic
3	#20259677	—	2	2	no	—
4	C₄×D₇₆₉	C₂²	1	1	yes	characteristic
5	#20259670	C₄	1	1	yes	characteristic
6	C₈×C₇₆₉	C₄	1	1	yes	characteristic
7	C₂×D₇₆₉	Q₈	1	1	yes	characteristic
8	C₄×C₇₆₉	C₂×C₄	1	1	yes	characteristic
9	Dic₇₆₉	D₄	1	1	yes	characteristic
10	C₂×C₇₆₉	C₄⋊C₄	1	1	yes	characteristic
11	D₇₆₉	—	2	1	no	—
12	C₇₆₉	#108	1	1	yes	characteristic, complemented, Sylow
13	#108	—	769	1	no	maximal, Sylow
14	M₁₆	—	769	2	no	—
15	C₂×C₈	—	769	1	no	—
16	C₂×C₄	—	769	1	no	—
17	C₈	—	769	1	no	—
18	C₈	—	1538	2	no	—
19	C₈	#15690484	1	1	yes	characteristic
20	C₂²	—	769	1	no	—
21	C₄	—	769	1	no	—
22	C₄	C₂×#15690484	1	1	yes	characteristic
23	C₂	—	1538	1	no	—
24	C₂	C₄⋊#15690484	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₇₆₉	#108	semidirect

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