Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
216 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 37 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. #11746727 | C2 | semidirect |
| 3. #11746725 | C2 | semidirect |
| 5. C3×C5×#127 | C4 | semidirect |
| 11. C3×#3935 | C4 | semidirect |
| 30. C5×#127 | Dic3 | semidirect |
| 36. #3935 | Dic3 | semidirect |
| 53. C3×#127 | AGL(1,𝔽5) | semidirect |
| 107. #127 | ΓL(1,𝔽16) | semidirect |
| 149. C3×C5 | #1406 | semidirect |
| 180. C5 | #67797 | semidirect |
| 190. C3 | #10598748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65363 | 2 |
| #11746727 | 2 |
| #11746725 | 2 |
| #10598748 | 3 |
| #67797 | 5 |