Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
268 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 268 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×#6769 | C2 | semidirect |
| 2. C3×#6765 | C2 | semidirect |
| 3. C3×#6706 | C2 | semidirect |
| 4. C3×C5×D3×C8 | C2 | semidirect |
| 5. C32×#677 | C2 | semidirect |
| 6. C3×#6662 | C2 | semidirect |
| 7. C3×#6653 | C2 | semidirect |
| 9. #91272 | C3 | direct (N × H) |
| 24. #6769 | C2×C3 | semidirect |
| 25. #6765 | C2×C3 | semidirect |
| 27. #6706 | C2×C3 | semidirect |
| 28. C5×D3×C8 | C2×C3 | semidirect |
| 33. C3×#677 | D3 | semidirect |
| 34. C3×#677 | C2×C3 | semidirect |
| 35. #6662 | C2×C3 | semidirect |
| 36. #6653 | C2×C3 | semidirect |
| 51. C3×D3×C8 | D5 | semidirect |
| 89. #677 | C3×D3 | semidirect |
| 132. D3×C8 | C3×D5 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 207. C3×C5 | #916 | semidirect |
| 208. C3×C5 | C3×#135 | semidirect |
| 230. C32 | #4050 | semidirect |
| 252. C5 | C3×#916 | semidirect |
| 261. C3 | #91272 | direct (N × H) |
| 262. C3 | C3×#4050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6769 | 2 |
| C3×#6765 | 2 |
| C3×#6706 | 2 |
| C3×C5×D3×C8 | 2 |
| C32×#677 | 2 |
| C3×#6662 | 2 |
| C3×#6653 | 2 |
| C3×#4050 | 3 |
| #91272 | 3 |
| C3×#916 | 5 |