Subgroups — Dic₁₇₁₂ #20292468

Order 6848.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₈₅₆	C₂	1	2	yes	maximal
2	C₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	Dic₄₂₈	—	2	2	no	—
4	C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
5	Dic₂₁₄	—	4	2	no	—
6	C₈×C₁₀₇	D₄	1	1	yes	characteristic
7	C₄×C₁₀₇	D₈	1	1	yes	characteristic
8	Dic₁₀₇	—	8	2	no	—
9	C₂×C₁₀₇	D₁₆	1	1	yes	characteristic
10	C₁₀₇	Q₆₄	1	1	yes	characteristic, complemented, Sylow
11	Q₆₄	—	107	1	no	maximal, Sylow
12	Q₃₂	—	107	2	no	—
13	C₃₂	D₁₀₇	1	1	yes	characteristic
14	Q₁₆	—	214	2	no	—
15	C₁₆	C₂×D₁₀₇	1	1	yes	characteristic
16	Q₈	—	428	2	no	—
17	C₈	D₄₂₈	1	1	yes	characteristic
18	C₄	—	856	2	no	—
19	C₄	D₈₅₆	1	1	yes	characteristic
20	C₂	D₁₇₁₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
10. C₁₀₇	Q₆₄	semidirect