Subgroups — Dic₁₆₉₆ #20272933

Order 6784.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₈₄₈	C₂	1	2	yes	maximal
2	C₅₃×C₆₄	C₂	1	1	yes	maximal, characteristic
3	Dic₄₂₄	—	2	2	no	—
4	C₃₂×C₅₃	C₂²	1	1	yes	characteristic
5	Dic₂₁₂	—	4	2	no	—
6	C₁₆×C₅₃	D₄	1	1	yes	characteristic
7	Dic₁₀₆	—	8	2	no	—
8	C₈×C₅₃	D₈	1	1	yes	characteristic
9	C₄×C₅₃	D₁₆	1	1	yes	characteristic
10	Dic₅₃	—	16	2	no	—
11	Q₁₂₈	—	53	1	no	maximal, Sylow
12	C₂×C₅₃	D₃₂	1	1	yes	characteristic
13	Q₆₄	—	53	2	no	—
14	C₆₄	D₅₃	1	1	yes	characteristic
15	C₅₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
16	Q₃₂	—	106	2	no	—
17	C₃₂	C₂×D₅₃	1	1	yes	characteristic
18	Q₁₆	—	212	2	no	—
19	C₁₆	D₂₁₂	1	1	yes	characteristic
20	Q₈	—	424	2	no	—
21	C₈	D₄₂₄	1	1	yes	characteristic
22	C₄	—	848	2	no	—
23	C₄	D₈₄₈	1	1	yes	characteristic
24	C₂	D₁₆₉₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₅₃	Q₁₂₈	semidirect