Subgroups — Dic₂₃₃₆ #22608149

Order 9344.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₁₆₈	C₂	1	2	yes	maximal
2	C₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
3	Dic₅₈₄	—	2	2	no	—
4	C₃₂×C₇₃	C₂²	1	1	yes	characteristic
5	Dic₂₉₂	—	4	2	no	—
6	C₁₆×C₇₃	D₄	1	1	yes	characteristic
7	Dic₁₄₆	—	8	2	no	—
8	C₈×C₇₃	D₈	1	1	yes	characteristic
9	C₄×C₇₃	D₁₆	1	1	yes	characteristic
10	Dic₇₃	—	16	2	no	—
11	C₂×C₇₃	D₃₂	1	1	yes	characteristic
12	Q₁₂₈	—	73	1	no	maximal, Sylow
13	C₇₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
14	Q₆₄	—	73	2	no	—
15	C₆₄	D₇₃	1	1	yes	characteristic
16	Q₃₂	—	146	2	no	—
17	C₃₂	C₂×D₇₃	1	1	yes	characteristic
18	Q₁₆	—	292	2	no	—
19	C₁₆	D₂₉₂	1	1	yes	characteristic
20	Q₈	—	584	2	no	—
21	C₈	D₅₈₄	1	1	yes	characteristic
22	C₄	—	1168	2	no	—
23	C₄	D₁₁₆₈	1	1	yes	characteristic
24	C₂	D₂₃₃₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. C₇₃	Q₁₂₈	semidirect