Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
404 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11746744 | C2 | semidirect |
| 5. C3×#64873 | C2 | semidirect |
| 6. #11746510 | C2 | semidirect |
| 7. #11746509 | C2 | semidirect |
| 35. #64873 | D3 | semidirect |
| 324. C3×C5 | #1544 | semidirect |
| 373. C5 | #68419 | semidirect |
| 390. C3 | #10604363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11753518 | 2 |
| #11751796 | 2 |
| #11746744 | 2 |
| C3×#64873 | 2 |
| #11746510 | 2 |
| #11746509 | 2 |
| #10604363 | 3 |
| #68419 | 5 |