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×C5×#237 | C2 | semidirect |
| 2. C3×#6765 | C2 | semidirect |
| 3. C3×#6716 | C2 | semidirect |
| 4. C32×#686 | C2 | semidirect |
| 5. C3×#6663 | C2 | semidirect |
| 6. C3×#6655 | C2 | semidirect |
| 7. C3×D3×#168 | C2 | semidirect |
| 9. #91493 | C3 | direct (N × H) |
| 23. C5×#237 | C2×C3 | semidirect |
| 25. #6765 | C2×C3 | semidirect |
| 26. #6716 | C2×C3 | semidirect |
| 31. C3×#686 | D3 | semidirect |
| 32. C3×#686 | C2×C3 | semidirect |
| 34. #6663 | C2×C3 | semidirect |
| 35. #6655 | C2×C3 | semidirect |
| 36. D3×#168 | C2×C3 | semidirect |
| 46. C3×#237 | D5 | semidirect |
| 88. #686 | C3×D3 | semidirect |
| 121. #237 | C3×D5 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 208. C3×C5 | #912 | semidirect |
| 209. C3×C5 | C3×#135 | semidirect |
| 231. C32 | #4096 | semidirect |
| 254. C5 | C3×#912 | semidirect |
| 263. C3 | #91493 | direct (N × H) |
| 264. C3 | C3×#4096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#237 | 2 |
| C3×#6765 | 2 |
| C3×#6716 | 2 |
| C32×#686 | 2 |
| C3×#6663 | 2 |
| C3×#6655 | 2 |
| C3×D3×#168 | 2 |
| C3×#4096 | 3 |
| #91493 | 3 |
| C3×#912 | 5 |