Subgroups — Dic₅₅₃₆ #36351781

Order 22144.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₇₆₈	C₂	1	2	yes	maximal
2	C₆₄×C₁₇₃	C₂	1	1	yes	maximal, characteristic
3	Dic₁₃₈₄	—	2	2	no	—
4	C₃₂×C₁₇₃	C₂²	1	1	yes	characteristic
5	Dic₆₉₂	—	4	2	no	—
6	C₁₆×C₁₇₃	D₄	1	1	yes	characteristic
7	Dic₃₄₆	—	8	2	no	—
8	C₈×C₁₇₃	D₈	1	1	yes	characteristic
9	C₄×C₁₇₃	D₁₆	1	1	yes	characteristic
10	Dic₁₇₃	—	16	2	no	—
11	C₂×C₁₇₃	D₃₂	1	1	yes	characteristic
12	C₁₇₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
13	Q₁₂₈	—	173	1	no	maximal, Sylow
14	Q₆₄	—	173	2	no	—
15	C₆₄	D₁₇₃	1	1	yes	characteristic
16	Q₃₂	—	346	2	no	—
17	C₃₂	C₂×D₁₇₃	1	1	yes	characteristic
18	Q₁₆	—	692	2	no	—
19	C₁₆	D₆₉₂	1	1	yes	characteristic
20	Q₈	—	1384	2	no	—
21	C₈	D₁₃₈₄	1	1	yes	characteristic
22	C₄	—	2768	2	no	—
23	C₄	D₂₇₆₈	1	1	yes	characteristic
24	C₂	D₅₅₃₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₁₇₃	Q₁₂₈	semidirect

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