Subgroups — Dic₁₀₄ #88041

Order 416.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅₂	C₂	1	2	yes	maximal
2	C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	Dic₂₆	—	2	2	no	—
4	C₈×C₁₃	C₂²	1	1	yes	characteristic
5	C₄×C₁₃	D₄	1	1	yes	characteristic
6	Dic₁₃	—	4	2	no	—
7	Q₃₂	—	13	1	no	maximal, Sylow
8	C₂×C₁₃	D₈	1	1	yes	characteristic
9	Q₁₆	—	13	2	no	—
10	C₁₆	D₁₃	1	1	yes	characteristic
11	C₁₃	Q₃₂	1	1	yes	characteristic, complemented, Sylow
12	Q₈	—	26	2	no	—
13	C₈	C₂×D₁₃	1	1	yes	characteristic
14	C₄	—	52	2	no	—
15	C₄	D₅₂	1	1	yes	characteristic
16	C₂	D₁₀₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
11. C₁₃	Q₃₂	semidirect

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