Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
304 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 2. C2×#6718 | C2 | semidirect |
| 3. C5×#946 | C2 | semidirect |
| 4. C2×C3×#688 | C2 | semidirect |
| 5. #90975 | C2 | semidirect |
| 6. #90964 | C2 | semidirect |
| 7. (C2×D3)⋊#168 | C2 | semidirect |
| 28. C2×#688 | D3 | semidirect |
| 53. #946 | D5 | semidirect |
| 180. C3×C5 | #452 | semidirect |
| 223. C5 | #5173 | semidirect |
| 237. C3 | #65336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6765 | 2 |
| C2×#6718 | 2 |
| C5×#946 | 2 |
| C2×C3×#688 | 2 |
| #90975 | 2 |
| #90964 | 2 |
| (C2×D3)⋊#168 | 2 |
| #65336 | 3 |
| #5173 | 5 |