Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
352 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #11751189 | C2 | semidirect |
| 2. #11751185 | C2 | semidirect |
| 4. #11750935 | C2 | semidirect |
| 5. C3×C5×#333 | C2 | semidirect |
| 6. #11746306 | C2 | semidirect |
| 7. #11746301 | C2 | semidirect |
| 29. C5×#333 | D3 | semidirect |
| 54. C3×#333 | D5 | semidirect |
| 133. #333 | D15 | semidirect |
| 263. C3×C5 | #1677 | semidirect |
| 310. C5 | #68498 | semidirect |
| 325. C3 | #10599291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751189 | 2 |
| #11751185 | 2 |
| #11750944 | 2 |
| #11750935 | 2 |
| C3×C5×#333 | 2 |
| #11746306 | 2 |
| #11746301 | 2 |
| #10599291 | 3 |
| #68498 | 5 |