Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 98 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. #11750981 | C2 | semidirect |
| 3. C2×#90933 | C2 | semidirect |
| 4. C5×#4492 | C2 | semidirect |
| 5. C3×#64711 | C2 | semidirect |
| 6. #11745900 | C2 | semidirect |
| 7. #11745892 | C2 | semidirect |
| 16. #91277 | C4 | semidirect |
| 30. #64711 | D3 | semidirect |
| 59. #4492 | D5 | semidirect |
| 261. C3×C5 | #2138 | semidirect |
| 303. C5 | #69188 | semidirect |
| 317. C3 | #10600013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91277 | 2 |
| #11750981 | 2 |
| C2×#90933 | 2 |
| C5×#4492 | 2 |
| C3×#64711 | 2 |
| #11745900 | 2 |
| #11745892 | 2 |
| #10600013 | 3 |
| #69188 | 5 |