Subgroups — Dic₉₆ #67435

Order 384.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₄₈	C₂	1	2	yes	maximal
2	C₃×C₆₄	C₂	1	1	yes	maximal, characteristic
3	Q₁₂₈	—	3	1	no	maximal, Sylow
4	Dic₂₄	—	2	2	no	—
5	C₃×C₃₂	C₂²	1	1	yes	characteristic
6	Q₆₄	—	3	2	no	—
7	C₆₄	D₃	1	1	yes	characteristic
8	Dic₁₂	—	4	2	no	—
9	C₃×C₁₆	D₄	1	1	yes	characteristic
10	Q₃₂	—	6	2	no	—
11	C₃₂	C₂×D₃	1	1	yes	characteristic
12	Dic₆	—	8	2	no	—
13	C₃×C₈	D₈	1	1	yes	characteristic
14	Q₁₆	—	12	2	no	—
15	C₁₆	D₁₂	1	1	yes	characteristic
16	C₃×C₄	D₁₆	1	1	yes	characteristic
17	Dic₃	—	16	2	no	—
18	Q₈	—	24	2	no	—
19	C₈	D₂₄	1	1	yes	characteristic
20	C₂×C₃	D₃₂	1	1	yes	characteristic
21	C₄	—	48	2	no	—
22	C₄	D₄₈	1	1	yes	characteristic
23	C₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
24	C₂	D₉₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
23. C₃	Q₁₂₈	semidirect

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