Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
424 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 4. #11746741 | C2 | semidirect |
| 5. C3×#64870 | C2 | semidirect |
| 6. #11746507 | C2 | semidirect |
| 7. #11746506 | C2 | semidirect |
| 35. #64870 | D3 | semidirect |
| 312. C3×C5 | #1531 | semidirect |
| 355. C5 | #68365 | semidirect |
| 370. C3 | #10604351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11753618 | 2 |
| D3×#4002 | 2 |
| #11751803 | 2 |
| #11746741 | 2 |
| C3×#64870 | 2 |
| #11746507 | 2 |
| #11746506 | 2 |
| #10604351 | 3 |
| #68365 | 5 |