Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 86 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. #11746299 | C2 | semidirect |
| 5. C3×#64698 | C2 | semidirect |
| 6. #11746017 | C2 | semidirect |
| 7. #11746015 | C2 | semidirect |
| 35. #64698 | D3 | semidirect |
| 375. C3×C5 | #2135 | semidirect |
| 432. C5 | #69173 | semidirect |
| 449. C3 | #10600943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11755162 | 2 |
| C5×#4751 | 2 |
| #11749372 | 2 |
| #11746299 | 2 |
| C3×#64698 | 2 |
| #11746017 | 2 |
| #11746015 | 2 |
| #10600943 | 3 |
| #69173 | 5 |