Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 70 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. #11746970 | C2 | semidirect |
| 4. #11746931 | C2 | semidirect |
| 5. #11746286 | C2 | semidirect |
| 6. C3×#64685 | C2 | semidirect |
| 35. #64685 | D3 | semidirect |
| 300. C3×C5 | #1664 | semidirect |
| 340. C5 | #68378 | semidirect |
| 354. C3 | #10602040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752653 | 2 |
| C5×#4714 | 2 |
| #11746970 | 2 |
| #11746931 | 2 |
| #11746286 | 2 |
| C3×#64685 | 2 |
| #11745847 | 2 |
| #10602040 | 3 |
| #68378 | 5 |