Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 1. C3×#6765 | C2 | semidirect |
| 2. C3×Dic60 | C2 | semidirect |
| 3. C3×C5×D3×C8 | C2 | semidirect |
| 4. C32×D40 | C2 | semidirect |
| 5. C3×#6657 | C2 | semidirect |
| 7. #91273 | C3 | direct (N × H) |
| 17. #6765 | C2×C3 | semidirect |
| 19. Dic60 | C2×C3 | semidirect |
| 20. C5×D3×C8 | C2×C3 | semidirect |
| 23. C3×D40 | D3 | semidirect |
| 24. C3×D40 | C2×C3 | semidirect |
| 26. #6657 | C2×C3 | semidirect |
| 37. C3×D3×C8 | D5 | semidirect |
| 62. D40 | C3×D3 | semidirect |
| 93. D3×C8 | C3×D5 | semidirect |
| 94. C32×C5 | #135 | semidirect |
| 146. C3×C5 | #912 | semidirect |
| 147. C3×C5 | C3×#135 | semidirect |
| 163. C32 | #4050 | semidirect |
| 179. C5 | C3×#912 | semidirect |
| 186. C3 | #91273 | direct (N × H) |
| 187. C3 | C3×#4050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6765 | 2 |
| C3×Dic60 | 2 |
| C3×C5×D3×C8 | 2 |
| C32×D40 | 2 |
| C3×#6657 | 2 |
| C3×#4050 | 3 |
| #91273 | 3 |
| C3×#912 | 5 |