Subgroups — Dic₃₅₆₈ #28383421

Order 14272.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₇₈₄	C₂	1	2	yes	maximal
2	C₃₂×C₂₂₃	C₂	1	1	yes	maximal, characteristic
3	Dic₈₉₂	—	2	2	no	—
4	C₁₆×C₂₂₃	C₂²	1	1	yes	characteristic
5	Dic₄₄₆	—	4	2	no	—
6	C₈×C₂₂₃	D₄	1	1	yes	characteristic
7	C₄×C₂₂₃	D₈	1	1	yes	characteristic
8	Dic₂₂₃	—	8	2	no	—
9	C₂×C₂₂₃	D₁₆	1	1	yes	characteristic
10	C₂₂₃	Q₆₄	1	1	yes	characteristic, complemented, Sylow
11	Q₆₄	—	223	1	no	maximal, Sylow
12	Q₃₂	—	223	2	no	—
13	C₃₂	D₂₂₃	1	1	yes	characteristic
14	Q₁₆	—	446	2	no	—
15	C₁₆	C₂×D₂₂₃	1	1	yes	characteristic
16	Q₈	—	892	2	no	—
17	C₈	D₈₉₂	1	1	yes	characteristic
18	C₄	—	1784	2	no	—
19	C₄	D₁₇₈₄	1	1	yes	characteristic
20	C₂	D₃₅₆₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
10. C₂₂₃	Q₆₄	semidirect

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