Subgroups — Dic₂₄ #801

Order 96.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₂	C₂	1	2	yes	maximal
2	C₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	Q₃₂	—	3	1	no	maximal, Sylow
4	Dic₆	—	2	2	no	—
5	C₃×C₈	C₂²	1	1	yes	characteristic
6	Q₁₆	—	3	2	no	—
7	C₁₆	D₃	1	1	yes	characteristic
8	C₃×C₄	D₄	1	1	yes	characteristic
9	Dic₃	—	4	2	no	—
10	Q₈	—	6	2	no	—
11	C₈	C₂×D₃	1	1	yes	characteristic
12	C₂×C₃	D₈	1	1	yes	characteristic
13	C₄	—	12	2	no	—
14	C₄	D₁₂	1	1	yes	characteristic
15	C₃	Q₃₂	1	1	yes	characteristic, complemented, Sylow
16	C₂	D₂₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₃	Q₃₂	semidirect

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