Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 270 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. C3×#6817 | C2 | semidirect |
| 2. C3×C5×#235 | C2 | semidirect |
| 3. C2×C32×#168 | C2 | semidirect |
| 4. C3×#6663 | C2 | semidirect |
| 5. C3×#6660 | C2 | semidirect |
| 6. C3×#6659 | C2 | semidirect |
| 7. C3×#6654 | C2 | semidirect |
| 9. #91303 | C3 | direct (N × H) |
| 23. #6817 | C2×C3 | semidirect |
| 24. C5×#235 | C2×C3 | semidirect |
| 31. C2×C3×#168 | D3 | semidirect |
| 32. C2×C3×#168 | C2×C3 | semidirect |
| 33. #6663 | C2×C3 | semidirect |
| 34. #6660 | C2×C3 | semidirect |
| 35. #6659 | C2×C3 | semidirect |
| 36. #6654 | C2×C3 | semidirect |
| 46. C3×#235 | D5 | semidirect |
| 89. C2×#168 | C3×D3 | semidirect |
| 121. #235 | C3×D5 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 207. C3×C5 | #904 | semidirect |
| 208. C3×C5 | C3×#135 | semidirect |
| 230. C32 | #4096 | semidirect |
| 252. C5 | C3×#904 | semidirect |
| 261. C3 | #91303 | direct (N × H) |
| 262. C3 | C3×#4096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6817 | 2 |
| C3×C5×#235 | 2 |
| C2×C32×#168 | 2 |
| C3×#6663 | 2 |
| C3×#6660 | 2 |
| C3×#6659 | 2 |
| C3×#6654 | 2 |
| C3×#4096 | 3 |
| #91303 | 3 |
| C3×#904 | 5 |