Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
472 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. #11752641 | C2 | semidirect |
| 2. #11751176 | C2 | semidirect |
| 4. C3×#65365 | C2 | semidirect |
| 5. #11745861 | C2 | semidirect |
| 6. #11745845 | C2 | semidirect |
| 7. #11745837 | C2 | semidirect |
| 29. #65365 | D3 | semidirect |
| 100. C5×D12 | SD16 | semidirect |
| 262. D12 | #687 | semidirect |
| 312. C3×C5 | #1622 | semidirect |
| 364. C5 | #71264 | semidirect |
| 381. C3 | #10601809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752641 | 2 |
| #11751176 | 2 |
| C5×#5072 | 2 |
| C3×#65365 | 2 |
| #11745861 | 2 |
| #11745845 | 2 |
| #11745837 | 2 |
| #10601809 | 3 |
| #71264 | 5 |