Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
168 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 48 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. #91275 | C2 | semidirect |
| 2. D240 | C2 | semidirect |
| 3. C5×D3×C16 | C2 | semidirect |
| 4. C3×Dic40 | C2 | semidirect |
| 5. #90943 | C2 | semidirect |
| 17. Dic40 | D3 | semidirect |
| 31. D3×C16 | D5 | semidirect |
| 86. C3×C5 | #508 | semidirect |
| 105. C5 | #4919 | semidirect |
| 111. C3 | #65193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91275 | 2 |
| D240 | 2 |
| C5×D3×C16 | 2 |
| C3×Dic40 | 2 |
| #90943 | 2 |
| #65193 | 3 |
| #4919 | 5 |