Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 66 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. #91833 | C2 | semidirect |
| 3. C2×C3×#689 | C2 | semidirect |
| 5. C2×#6662 | C2 | semidirect |
| 7. #90954 | C2 | semidirect |
| 25. C2×#689 | D3 | semidirect |
| 153. C3×C5 | #497 | semidirect |
| 185. C5 | #5190 | semidirect |
| 195. C3 | #65456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91833 | 2 |
| C2×C5×#215 | 2 |
| C2×C3×#689 | 2 |
| #91370 | 2 |
| C2×#6662 | 2 |
| C2×#6659 | 2 |
| #90954 | 2 |
| #65456 | 3 |
| #5190 | 5 |