Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 92 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×#6762 | C2 | semidirect |
| 3. C2×C32×#170 | C2 | semidirect |
| 4. C3×#6740 | C2 | semidirect |
| 5. C3×#6739 | C2 | semidirect |
| 6. C3×#6738 | C2 | semidirect |
| 7. C3×D3×#170 | C2 | semidirect |
| 9. #91927 | C3 | direct (N × H) |
| 24. #6762 | C2×C3 | semidirect |
| 29. C2×C3×#170 | D3 | semidirect |
| 30. C2×C3×#170 | C2×C3 | semidirect |
| 33. #6740 | C2×C3 | semidirect |
| 34. #6739 | C2×C3 | semidirect |
| 35. #6738 | C2×C3 | semidirect |
| 36. D3×#170 | C2×C3 | semidirect |
| 87. C2×#170 | C3×D3 | semidirect |
| 133. C32×C5 | #131 | semidirect |
| 207. C3×C5 | #901 | semidirect |
| 208. C3×C5 | C3×#131 | semidirect |
| 230. C32 | #4131 | semidirect |
| 252. C5 | C3×#901 | semidirect |
| 261. C3 | #91927 | direct (N × H) |
| 262. C3 | C3×#4131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6782 | 2 |
| C3×#6762 | 2 |
| C2×C32×#170 | 2 |
| C3×#6740 | 2 |
| C3×#6739 | 2 |
| C3×#6738 | 2 |
| C3×D3×#170 | 2 |
| C3×#4131 | 3 |
| #91927 | 3 |
| C3×#901 | 5 |