Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11750975 | C2 | semidirect |
| 3. C3×C5×#357 | C2 | semidirect |
| 4. #11746383 | C2 | semidirect |
| 5. #11746330 | C2 | semidirect |
| 6. C16×Dic15 | C2 | semidirect |
| 7. #11746312 | C2 | semidirect |
| 23. C5×#357 | D3 | semidirect |
| 48. C3×#357 | D5 | semidirect |
| 116. #357 | D15 | semidirect |
| 230. C3×C5 | #2240 | semidirect |
| 271. C5 | #69183 | semidirect |
| 285. C3 | #10599976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751252 | 2 |
| #11750975 | 2 |
| C3×C5×#357 | 2 |
| #11746383 | 2 |
| #11746330 | 2 |
| C16×Dic15 | 2 |
| #11746312 | 2 |
| #10599976 | 3 |
| #69183 | 5 |