Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
392 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 120 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. #91759 | C2 | semidirect |
| 3. C3×#4016 | C2 | semidirect |
| 4. #91436 | C2 | semidirect |
| 6. #91417 | C2 | semidirect |
| 7. #91342 | C2 | semidirect |
| 8. #91341 | C2 | semidirect |
| 9. #91329 | C2 | semidirect |
| 41. #4016 | D3 | semidirect |
| 191. C3×C5 | #563 | semidirect |
| 225. C5 | #5699 | semidirect |
| 238. C3 | #66006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91759 | 2 |
| C5×#875 | 2 |
| C3×#4016 | 2 |
| #91436 | 2 |
| #91423 | 2 |
| #91417 | 2 |
| #91342 | 2 |
| #91341 | 2 |
| #91329 | 2 |
| #66006 | 3 |
| #5699 | 5 |