Subgroups — Dic₃₄₈₈ #28361250

Order 13952.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₇₄₄	C₂	1	2	yes	maximal
2	C₆₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic
3	Dic₈₇₂	—	2	2	no	—
4	C₃₂×C₁₀₉	C₂²	1	1	yes	characteristic
5	Dic₄₃₆	—	4	2	no	—
6	C₁₆×C₁₀₉	D₄	1	1	yes	characteristic
7	Dic₂₁₈	—	8	2	no	—
8	C₈×C₁₀₉	D₈	1	1	yes	characteristic
9	C₄×C₁₀₉	D₁₆	1	1	yes	characteristic
10	Dic₁₀₉	—	16	2	no	—
11	C₂×C₁₀₉	D₃₂	1	1	yes	characteristic
12	Q₁₂₈	—	109	1	no	maximal, Sylow
13	C₁₀₉	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
14	Q₆₄	—	109	2	no	—
15	C₆₄	D₁₀₉	1	1	yes	characteristic
16	Q₃₂	—	218	2	no	—
17	C₃₂	C₂×D₁₀₉	1	1	yes	characteristic
18	Q₁₆	—	436	2	no	—
19	C₁₆	D₄₃₆	1	1	yes	characteristic
20	Q₈	—	872	2	no	—
21	C₈	D₈₇₂	1	1	yes	characteristic
22	C₄	—	1744	2	no	—
23	C₄	D₁₇₄₄	1	1	yes	characteristic
24	C₂	D₃₄₈₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. C₁₀₉	Q₁₂₈	semidirect

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