Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
208 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #91992 | C2 | semidirect |
| 2. #91990 | C2 | semidirect |
| 4. #91239 | C2 | semidirect |
| 5. #91237 | C2 | semidirect |
| 6. #91225 | C2 | semidirect |
| 7. #91221 | C2 | semidirect |
| 19. C3×C5×SD16 | C4 | semidirect |
| 20. C3×#689 | C4 | semidirect |
| 21. C3×#686 | C4 | semidirect |
| 22. C3×#677 | C4 | semidirect |
| 65. C5×SD16 | Dic3 | semidirect |
| 66. #689 | Dic3 | semidirect |
| 67. #686 | Dic3 | semidirect |
| 68. #677 | Dic3 | semidirect |
| 83. C3×SD16 | AGL(1,𝔽5) | semidirect |
| 149. SD16 | ΓL(1,𝔽16) | semidirect |
| 160. C3×C5 | #444 | semidirect |
| 193. C5 | #5197 | semidirect |
| 202. C3 | #65737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91992 | 2 |
| #91990 | 2 |
| C3×#4062 | 2 |
| #91239 | 2 |
| #91237 | 2 |
| #91225 | 2 |
| #91221 | 2 |
| #65737 | 3 |
| #5197 | 5 |