Subgroups — Dic₃₃₉₂ #27272010

Order 13568.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₆₉₆	C₂	1	2	yes	maximal
2	C₅₃×C₁₂₈	C₂	1	1	yes	maximal, characteristic
3	Dic₈₄₈	—	2	2	no	—
4	C₅₃×C₆₄	C₂²	1	1	yes	characteristic
5	Dic₄₂₄	—	4	2	no	—
6	C₃₂×C₅₃	D₄	1	1	yes	characteristic
7	Dic₂₁₂	—	8	2	no	—
8	C₁₆×C₅₃	D₈	1	1	yes	characteristic
9	Dic₁₀₆	—	16	2	no	—
10	C₈×C₅₃	D₁₆	1	1	yes	characteristic
11	Q₂₅₆	—	53	1	no	maximal, Sylow
12	C₄×C₅₃	D₃₂	1	1	yes	characteristic
13	Dic₅₃	—	32	2	no	—
14	Q₁₂₈	—	53	2	no	—
15	C₁₂₈	D₅₃	1	1	yes	characteristic
16	C₂×C₅₃	D₆₄	1	1	yes	characteristic
17	Q₆₄	—	106	2	no	—
18	C₆₄	C₂×D₅₃	1	1	yes	characteristic
19	C₅₃	Q₂₅₆	1	1	yes	characteristic, complemented, Sylow
20	Q₃₂	—	212	2	no	—
21	C₃₂	D₂₁₂	1	1	yes	characteristic
22	Q₁₆	—	424	2	no	—
23	C₁₆	D₄₂₄	1	1	yes	characteristic
24	Q₈	—	848	2	no	—
25	C₈	D₈₄₈	1	1	yes	characteristic
26	C₄	—	1696	2	no	—
27	C₄	D₁₆₉₆	1	1	yes	characteristic
28	C₂	D₃₃₉₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₅₃	Q₂₅₆	semidirect

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