Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
496 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 496 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. #92098 | C2 | semidirect |
| 2. #92004 | C2 | semidirect |
| 3. C5×#942 | C2 | semidirect |
| 4. C2×C3×#689 | C2 | semidirect |
| 5. #91524 | C2 | semidirect |
| 6. #91523 | C2 | semidirect |
| 7. #91512 | C2 | semidirect |
| 8. #91511 | C2 | semidirect |
| 9. #91315 | C2 | semidirect |
| 10. #91303 | C2 | semidirect |
| 11. #91290 | C2 | semidirect |
| 47. C2×#689 | D3 | semidirect |
| 88. #942 | D5 | semidirect |
| 281. C3×C5 | #578 | semidirect |
| 333. C5 | #5766 | semidirect |
| 345. C3 | #66113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #92098 | 2 |
| #92004 | 2 |
| C5×#942 | 2 |
| C2×C3×#689 | 2 |
| #91524 | 2 |
| #91523 | 2 |
| #91512 | 2 |
| #91511 | 2 |
| #91315 | 2 |
| #91303 | 2 |
| #91290 | 2 |
| #66113 | 3 |
| #5766 | 5 |