Subgroups — Dic₅₂₁₆ #35212754

Order 20864.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₆₀₈	C₂	1	2	yes	maximal
2	C₆₄×C₁₆₃	C₂	1	1	yes	maximal, characteristic
3	Dic₁₃₀₄	—	2	2	no	—
4	C₃₂×C₁₆₃	C₂²	1	1	yes	characteristic
5	Dic₆₅₂	—	4	2	no	—
6	C₁₆×C₁₆₃	D₄	1	1	yes	characteristic
7	Dic₃₂₆	—	8	2	no	—
8	C₈×C₁₆₃	D₈	1	1	yes	characteristic
9	C₄×C₁₆₃	D₁₆	1	1	yes	characteristic
10	Dic₁₆₃	—	16	2	no	—
11	C₂×C₁₆₃	D₃₂	1	1	yes	characteristic
12	C₁₆₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
13	Q₁₂₈	—	163	1	no	maximal, Sylow
14	Q₆₄	—	163	2	no	—
15	C₆₄	D₁₆₃	1	1	yes	characteristic
16	Q₃₂	—	326	2	no	—
17	C₃₂	C₂×D₁₆₃	1	1	yes	characteristic
18	Q₁₆	—	652	2	no	—
19	C₁₆	D₆₅₂	1	1	yes	characteristic
20	Q₈	—	1304	2	no	—
21	C₈	D₁₃₀₄	1	1	yes	characteristic
22	C₄	—	2608	2	no	—
23	C₄	D₂₆₀₈	1	1	yes	characteristic
24	C₂	D₅₂₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₁₆₃	Q₁₂₈	semidirect

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