Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 3. #11746957 | C2 | semidirect |
| 4. #11746931 | C2 | semidirect |
| 6. #11745851 | C2 | semidirect |
| 7. #11745851 | C2 | semidirect |
| 300. C3×C5 | #1664 | semidirect |
| 340. C5 | #68359 | semidirect |
| 354. C3 | #10602040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756431 | 2 |
| C5×#5055 | 2 |
| #11746957 | 2 |
| #11746931 | 2 |
| C3×#64760 | 2 |
| #11745851 | 2 |
| #10602040 | 3 |
| #68359 | 5 |