Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
260 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 260 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 |
|---|---|---|
| 1. C2×C3×Dic30 | C2 | semidirect |
| 3. C32×#681 | C2 | semidirect |
| 4. C3×#6663 | C2 | semidirect |
| 5. C3×#6659 | C2 | semidirect |
| 7. #91322 | C3 | direct (N × H) |
| 19. C2×Dic30 | C2×C3 | semidirect |
| 25. C3×#681 | D3 | semidirect |
| 26. C3×#681 | C2×C3 | semidirect |
| 27. #6663 | C2×C3 | semidirect |
| 28. #6659 | C2×C3 | semidirect |
| 70. #681 | C3×D3 | semidirect |
| 106. C32×C5 | #137 | semidirect |
| 166. C3×C5 | #909 | semidirect |
| 167. C3×C5 | C3×#137 | semidirect |
| 186. C32 | #4097 | semidirect |
| 204. C5 | C3×#909 | semidirect |
| 212. C3 | #91322 | direct (N × H) |
| 213. C3 | C3×#4097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic30 | 2 |
| C3×C5×#235 | 2 |
| C32×#681 | 2 |
| C3×#6663 | 2 |
| C3×#6659 | 2 |
| C3×#4097 | 3 |
| #91322 | 3 |
| C3×#909 | 5 |