Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
260 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3×D5×Dic6 | C2 | semidirect |
| 3. C3×Dic60 | C2 | semidirect |
| 4. C3×C5×#204 | C2 | semidirect |
| 5. C32×#676 | C2 | semidirect |
| 6. C3×#6663 | C2 | semidirect |
| 7. C3×#6659 | C2 | semidirect |
| 9. #91260 | C3 | direct (N × H) |
| 25. D5×Dic6 | C2×C3 | semidirect |
| 27. Dic60 | C2×C3 | semidirect |
| 28. C5×#204 | C2×C3 | semidirect |
| 33. C3×#676 | D3 | semidirect |
| 34. C3×#676 | C2×C3 | semidirect |
| 35. #6663 | C2×C3 | semidirect |
| 36. #6659 | C2×C3 | semidirect |
| 51. C3×#204 | D5 | semidirect |
| 88. #676 | C3×D3 | semidirect |
| 131. #204 | C3×D5 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 203. C3×C5 | #909 | semidirect |
| 204. C3×C5 | C3×#137 | semidirect |
| 225. C32 | #4061 | semidirect |
| 245. C5 | C3×#909 | semidirect |
| 254. C3 | #91260 | direct (N × H) |
| 255. C3 | C3×#4061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6772 | 2 |
| C3×D5×Dic6 | 2 |
| C3×Dic60 | 2 |
| C3×C5×#204 | 2 |
| C32×#676 | 2 |
| C3×#6663 | 2 |
| C3×#6659 | 2 |
| C3×#4061 | 3 |
| #91260 | 3 |
| C3×#909 | 5 |