Subgroups — #22608148

Order 9344.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₁₆₈	C₂	1	1	yes	maximal, characteristic
2	#17988306	C₂	1	1	yes	maximal, characteristic
3	Q₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
4	Dic₅₈₄	—	2	1	no	—
5	Q₃₂×C₇₃	—	2	1	no	—
6	C₃₂×C₇₃	C₂²	1	1	yes	characteristic
7	Dic₂₉₂	—	4	1	no	—
8	Q₁₆×C₇₃	—	4	1	no	—
9	C₁₆×C₇₃	D₄	1	1	yes	characteristic
10	Q₈×C₇₃	—	8	1	no	—
11	Dic₁₄₆	—	8	1	no	—
12	C₈×C₇₃	D₈	1	1	yes	characteristic
13	C₄×C₇₃	—	16	1	no	—
14	C₄×C₇₃	D₁₆	1	1	yes	characteristic
15	Dic₇₃	—	16	1	no	—
16	C₂×C₇₃	D₃₂	1	1	yes	characteristic
17	Q₁₂₈	—	73	1	no	maximal, Sylow
18	C₇₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	Q₆₄	—	73	1	no	—
20	Q₆₄	D₇₃	1	1	yes	characteristic
21	C₆₄	—	73	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	146	1	no	—
24	C₃₂	C₂×D₇₃	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	292	1	no	—
27	C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	584	1	no	—
30	C₈	#11924013	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	1168	1	no	—
33	C₄	#14556532	1	1	yes	characteristic
34	C₂	#17988422	1	1	yes	characteristic

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

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