Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11751907 | C2 | semidirect |
| 3. #11751803 | C2 | semidirect |
| 4. #11746792 | C2 | semidirect |
| 5. C3×#64921 | C2 | semidirect |
| 6. #11746507 | C2 | semidirect |
| 7. #11746506 | C2 | semidirect |
| 33. #64921 | D3 | semidirect |
| 323. C3×C5 | #1529 | semidirect |
| 372. C5 | #68344 | semidirect |
| 389. C3 | #10604474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11754873 | 2 |
| #11751907 | 2 |
| #11751803 | 2 |
| #11746792 | 2 |
| C3×#64921 | 2 |
| #11746507 | 2 |
| #11746506 | 2 |
| #10604474 | 3 |
| #68344 | 5 |