Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 288 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 |
|---|---|---|
| 2. C3×#65485 | C2 | semidirect |
| 3. #11748064 | C2 | semidirect |
| 4. C5×#4567 | C2 | semidirect |
| 5. #11745946 | C2 | semidirect |
| 6. #11745907 | C2 | semidirect |
| 7. #11745873 | C2 | semidirect |
| 13. #91113 | C4 | semidirect |
| 14. #91112 | C4 | semidirect |
| 15. #91111 | C4 | semidirect |
| 16. #91110 | C4 | semidirect |
| 25. #65485 | D3 | semidirect |
| 55. #4567 | D5 | semidirect |
| 240. C3×C5 | #2179 | semidirect |
| 273. C5 | #70922 | semidirect |
| 282. C3 | #10600032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751295 | 2 |
| C3×#65485 | 2 |
| #11748064 | 2 |
| C5×#4567 | 2 |
| #11745946 | 2 |
| #11745907 | 2 |
| #11745873 | 2 |
| #10600032 | 3 |
| #70922 | 5 |