Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 84 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. #11746802 | C2 | semidirect |
| 5. C3×#64931 | C2 | semidirect |
| 6. #11746510 | C2 | semidirect |
| 7. #11746509 | C2 | semidirect |
| 33. #64931 | D3 | semidirect |
| 324. C3×C5 | #1554 | semidirect |
| 373. C5 | #68486 | semidirect |
| 390. C3 | #10604519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11755181 | 2 |
| #11751804 | 2 |
| #11751796 | 2 |
| #11746802 | 2 |
| C3×#64931 | 2 |
| #11746510 | 2 |
| #11746509 | 2 |
| #10604519 | 3 |
| #68486 | 5 |