Subgroups — #37589972

Order 24608.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27134384	C₂	1	2	yes	maximal, complemented
2	C₈×D₇₆₉	C₂	1	1	yes	maximal, characteristic
3	C₄×D₇₆₉	C₄	1	1	yes	characteristic
4	#20259670	C₂²	1	1	yes	characteristic
5	C₈×C₇₆₉	C₄	1	1	yes	characteristic
6	C₂×D₇₆₉	C₈	1	1	yes	characteristic
7	C₄×C₇₆₉	C₂×C₄	1	1	yes	characteristic
8	Dic₇₆₉	C₈	1	1	yes	characteristic
9	C₂×C₇₆₉	C₂×C₈	1	1	yes	characteristic
10	D₇₆₉	C₁₆	1	2	yes	complemented
11	C₇₆₉	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₁₆	—	769	1	no	maximal, Sylow
13	C₂×C₈	—	769	1	no	—
14	C₁₆	—	769	2	no	—
15	C₂×C₄	—	769	1	no	—
16	C₈	—	769	1	no	—
17	C₈	#15690484	1	1	yes	characteristic
18	C₂²	—	769	1	no	—
19	C₄	—	769	1	no	—
20	C₄	C₂×#15690484	1	1	yes	characteristic
21	C₂	—	769	2	no	—
22	C₂	#27134389	1	1	yes	characteristic

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

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