Subgroups — Dic₃₂₉₆ #27193362

Order 13184.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₆₄₈	C₂	1	2	yes	maximal
2	C₆₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	Dic₈₂₄	—	2	2	no	—
4	C₃₂×C₁₀₃	C₂²	1	1	yes	characteristic
5	Dic₄₁₂	—	4	2	no	—
6	C₁₆×C₁₀₃	D₄	1	1	yes	characteristic
7	Dic₂₀₆	—	8	2	no	—
8	C₈×C₁₀₃	D₈	1	1	yes	characteristic
9	C₄×C₁₀₃	D₁₆	1	1	yes	characteristic
10	Dic₁₀₃	—	16	2	no	—
11	C₂×C₁₀₃	D₃₂	1	1	yes	characteristic
12	Q₁₂₈	—	103	1	no	maximal, Sylow
13	C₁₀₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
14	Q₆₄	—	103	2	no	—
15	C₆₄	D₁₀₃	1	1	yes	characteristic
16	Q₃₂	—	206	2	no	—
17	C₃₂	C₂×D₁₀₃	1	1	yes	characteristic
18	Q₁₆	—	412	2	no	—
19	C₁₆	D₄₁₂	1	1	yes	characteristic
20	Q₈	—	824	2	no	—
21	C₈	D₈₂₄	1	1	yes	characteristic
22	C₄	—	1648	2	no	—
23	C₄	D₁₆₄₈	1	1	yes	characteristic
24	C₂	D₃₂₉₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. C₁₀₃	Q₁₂₈	semidirect

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