Subgroups — Dic₄₁₉₂ #30664179

Order 16768.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₀₉₆	C₂	1	2	yes	maximal
2	C₆₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	Dic₁₀₄₈	—	2	2	no	—
4	C₃₂×C₁₃₁	C₂²	1	1	yes	characteristic
5	Dic₅₂₄	—	4	2	no	—
6	C₁₆×C₁₃₁	D₄	1	1	yes	characteristic
7	Dic₂₆₂	—	8	2	no	—
8	C₈×C₁₃₁	D₈	1	1	yes	characteristic
9	C₄×C₁₃₁	D₁₆	1	1	yes	characteristic
10	Dic₁₃₁	—	16	2	no	—
11	C₂×C₁₃₁	D₃₂	1	1	yes	characteristic
12	C₁₃₁	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
13	Q₁₂₈	—	131	1	no	maximal, Sylow
14	Q₆₄	—	131	2	no	—
15	C₆₄	D₁₃₁	1	1	yes	characteristic
16	Q₃₂	—	262	2	no	—
17	C₃₂	C₂×D₁₃₁	1	1	yes	characteristic
18	Q₁₆	—	524	2	no	—
19	C₁₆	D₅₂₄	1	1	yes	characteristic
20	Q₈	—	1048	2	no	—
21	C₈	D₁₀₄₈	1	1	yes	characteristic
22	C₄	—	2096	2	no	—
23	C₄	D₂₀₉₆	1	1	yes	characteristic
24	C₂	D₄₁₉₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₁₃₁	Q₁₂₈	semidirect

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