Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
300 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 4. #11746754 | C2 | semidirect |
| 5. C3×#64881 | C2 | semidirect |
| 6. #11746515 | C2 | semidirect |
| 7. #11746514 | C2 | semidirect |
| 31. #64881 | D3 | semidirect |
| 240. C3×C5 | #1572 | semidirect |
| 281. C5 | #68533 | semidirect |
| 294. C3 | #10603899 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751807 | 2 |
| #11751754 | 2 |
| #11747579 | 2 |
| #11746754 | 2 |
| C3×#64881 | 2 |
| #11746515 | 2 |
| #11746514 | 2 |
| #10603899 | 3 |
| #68533 | 5 |