Subgroups — #22608147

Order 9344.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₁₆₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₃₃₆	C₂	1	1	yes	maximal, characteristic
3	C₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₅₈₄	—	2	1	no	—
5	D₁₁₆₈	—	2	1	no	—
6	C₃₂×C₇₃	C₂²	1	1	yes	characteristic
7	Dic₂₉₂	—	4	1	no	—
8	D₅₈₄	—	4	1	no	—
9	C₁₆×C₇₃	D₄	1	1	yes	characteristic
10	D₂₉₂	—	8	1	no	—
11	Dic₁₄₆	—	8	1	no	—
12	C₈×C₇₃	D₈	1	1	yes	characteristic
13	C₂×D₇₃	—	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	D₇₃	—	32	1	no	—
18	SD₁₂₈	—	73	1	no	maximal, Sylow
19	C₇₃	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
20	Q₆₄	—	73	1	no	—
21	D₃₂	—	73	1	no	—
22	C₆₄	D₇₃	1	1	yes	characteristic, complemented
23	Q₃₂	—	146	1	no	—
24	D₁₆	—	146	1	no	—
25	C₃₂	C₂×D₇₃	1	1	yes	characteristic
26	Q₁₆	—	292	1	no	—
27	D₈	—	292	1	no	—
28	C₁₆	D₂₉₂	1	1	yes	characteristic
29	Q₈	—	584	1	no	—
30	D₄	—	584	1	no	—
31	C₈	D₅₈₄	1	1	yes	characteristic
32	C₂²	—	1168	1	no	—
33	C₄	—	1168	1	no	—
34	C₄	D₁₁₆₈	1	1	yes	characteristic
35	C₂	—	2336	1	no	—
36	C₂	D₂₃₃₆	1	1	yes	characteristic

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