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. #11746755 | C2 | semidirect |
| 5. C3×#64882 | C2 | semidirect |
| 6. #11746513 | C2 | semidirect |
| 7. #11746512 | C2 | semidirect |
| 30. #64882 | D3 | semidirect |
| 240. C3×C5 | #1572 | semidirect |
| 281. C5 | #68573 | semidirect |
| 294. C3 | #10604017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751791 | 2 |
| #11751777 | 2 |
| #11747583 | 2 |
| #11746755 | 2 |
| C3×#64882 | 2 |
| #11746513 | 2 |
| #11746512 | 2 |
| #10604017 | 3 |
| #68573 | 5 |