Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
432 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 128 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. D4×Dic15 | C2 | semidirect |
| 3. C3×#4082 | C2 | semidirect |
| 4. #91576 | C2 | semidirect |
| 5. #91543 | C2 | semidirect |
| 6. #91531 | C2 | semidirect |
| 7. #91525 | C2 | semidirect |
| 8. #91468 | C2 | semidirect |
| 9. #91371 | C2 | semidirect |
| 10. #91369 | C2 | semidirect |
| 11. #91331 | C2 | semidirect |
| 39. #4082 | D3 | semidirect |
| 228. C3×C5 | #542 | semidirect |
| 272. C5 | #5682 | semidirect |
| 289. C3 | #65937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic15 | 2 |
| C5×#938 | 2 |
| C3×#4082 | 2 |
| #91576 | 2 |
| #91543 | 2 |
| #91531 | 2 |
| #91525 | 2 |
| #91468 | 2 |
| #91371 | 2 |
| #91369 | 2 |
| #91331 | 2 |
| #65937 | 3 |
| #5682 | 5 |