Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 4. C5×#808 | C2 | semidirect |
| 5. C3×#3939 | C2 | semidirect |
| 6. #90988 | C2 | semidirect |
| 7. #90987 | C2 | semidirect |
| 20. #6648 | C4 | semidirect |
| 28. #3939 | D3 | semidirect |
| 46. #808 | D5 | semidirect |
| 139. C3×C5 | #427 | semidirect |
| 170. C5 | #4880 | semidirect |
| 182. C3 | #65149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91781 | 2 |
| #91347 | 2 |
| C2×#6648 | 2 |
| C5×#808 | 2 |
| C3×#3939 | 2 |
| #90988 | 2 |
| #90987 | 2 |
| #65149 | 3 |
| #4880 | 5 |