Subgroups — Dic₂₆₀₈ #23781506

Order 10432.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₃₀₄	C₂	1	2	yes	maximal
2	C₃₂×C₁₆₃	C₂	1	1	yes	maximal, characteristic
3	Dic₆₅₂	—	2	2	no	—
4	C₁₆×C₁₆₃	C₂²	1	1	yes	characteristic
5	Dic₃₂₆	—	4	2	no	—
6	C₈×C₁₆₃	D₄	1	1	yes	characteristic
7	C₄×C₁₆₃	D₈	1	1	yes	characteristic
8	Dic₁₆₃	—	8	2	no	—
9	C₂×C₁₆₃	D₁₆	1	1	yes	characteristic
10	C₁₆₃	Q₆₄	1	1	yes	characteristic, complemented, Sylow
11	Q₆₄	—	163	1	no	maximal, Sylow
12	Q₃₂	—	163	2	no	—
13	C₃₂	D₁₆₃	1	1	yes	characteristic
14	Q₁₆	—	326	2	no	—
15	C₁₆	C₂×D₁₆₃	1	1	yes	characteristic
16	Q₈	—	652	2	no	—
17	C₈	D₆₅₂	1	1	yes	characteristic
18	C₄	—	1304	2	no	—
19	C₄	D₁₃₀₄	1	1	yes	characteristic
20	C₂	D₂₆₀₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
10. C₁₆₃	Q₆₄	semidirect