Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 92 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. C3×#65381 | C2 | semidirect |
| 5. #11746368 | C2 | semidirect |
| 6. #11745867 | C2 | semidirect |
| 7. #11745855 | C2 | semidirect |
| 26. #65381 | D3 | semidirect |
| 83. C5×D12 | Q16 | semidirect |
| 217. D12 | #689 | semidirect |
| 256. C3×C5 | #1669 | semidirect |
| 297. C5 | #71305 | semidirect |
| 310. C3 | #10601894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5087 | 2 |
| C3×#65381 | 2 |
| D12×#168 | 2 |
| #11746900 | 2 |
| #11746368 | 2 |
| #11745867 | 2 |
| #11745855 | 2 |
| #10601894 | 3 |
| #71305 | 5 |