Subgroups — C₄⋊#20259677 #37589965

Order 24608.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259677	C₂	1	2	yes	maximal
2	C₄×Dic₇₆₉	C₂	1	1	yes	maximal, characteristic
3	#20259677	—	2	2	no	—
4	C₂×Dic₇₆₉	C₄	1	1	yes	characteristic
5	C₂×Dic₇₆₉	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₇₆₉	C₄	1	1	yes	characteristic
7	C₂²×C₇₆₉	C₂×C₄	1	1	yes	characteristic
8	C₄×C₇₆₉	C₈	1	2	yes	complemented
9	Dic₇₆₉	—	2	1	no	—
10	Dic₇₆₉	D₄	1	1	yes	characteristic
11	Dic₇₆₉	Q₈	1	1	yes	characteristic
12	C₂×C₇₆₉	C₄⋊C₄	1	1	yes	characteristic
13	C₂×C₇₆₉	C₂×C₈	1	1	yes	characteristic
14	C₂×C₇₆₉	M₁₆	1	1	yes	characteristic
15	C₇₆₉	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
16	C₄⋊C₈	—	769	1	no	maximal, Sylow
17	C₂×C₈	—	769	2	no	—
18	C₄²	—	769	1	no	—
19	C₂×C₄	—	769	1	no	—
20	C₂×C₄	—	769	1	no	—
21	C₂×C₄	#15690484	1	1	yes	characteristic
22	C₈	—	1538	2	no	—
23	C₂²	C₂×#15690484	1	1	yes	characteristic
24	C₄	—	769	1	no	—
25	C₄	—	769	1	no	—
26	C₄	—	1538	1	no	—
27	C₄	#20259677	1	2	yes	complemented
28	C₂	C₄⋊#15690484	1	1	yes	characteristic
29	C₂	C₂×#20259677	1	1	yes	characteristic
30	C₂	#27134391	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.