Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
400 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 84 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. #11746940 | C2 | semidirect |
| 3. #11746940 | C2 | semidirect |
| 4. C5×#4543 | C2 | semidirect |
| 5. C3×#64763 | C2 | semidirect |
| 6. #11745848 | C2 | semidirect |
| 7. #11745848 | C2 | semidirect |
| 33. #64763 | D3 | semidirect |
| 67. #4543 | D5 | semidirect |
| 319. C3×C5 | #1535 | semidirect |
| 368. C5 | #68368 | semidirect |
| 385. C3 | #10599161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756450 | 2 |
| #11746940 | 2 |
| C5×#4543 | 2 |
| C3×#64763 | 2 |
| #11745848 | 2 |
| #10599161 | 3 |
| #68368 | 5 |