Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 86 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. #11750806 | C2 | semidirect |
| 3. #11746983 | C2 | semidirect |
| 4. C5×#4464 | C2 | semidirect |
| 5. C3×#64684 | C2 | semidirect |
| 6. #11745847 | C2 | semidirect |
| 7. #11745846 | C2 | semidirect |
| 35. #64684 | D3 | semidirect |
| 72. #4464 | D5 | semidirect |
| 354. C3×C5 | #1530 | semidirect |
| 413. C5 | #68345 | semidirect |
| 432. C3 | #10599138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752678 | 2 |
| #11750806 | 2 |
| #11746983 | 2 |
| C5×#4464 | 2 |
| C3×#64684 | 2 |
| #11745847 | 2 |
| #11745846 | 2 |
| #10599138 | 3 |
| #68345 | 5 |