Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 326 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×D5×D12 | C2 | semidirect |
| 2. C3×D120 | C2 | semidirect |
| 3. C3×C5×D24 | C2 | semidirect |
| 4. C32×C8×D5 | C2 | semidirect |
| 5. C3×#6654 | C2 | semidirect |
| 7. D5×D24 | C3 | direct (N × H) |
| 9. C3×D60 | C22 | semidirect |
| 10. C3×C5×D12 | C22 | semidirect |
| 13. C32×C5×C8 | C22 | semidirect |
| 14. C32×#168 | C22 | semidirect |
| 17. D5×D12 | C2×C3 | semidirect |
| 19. D120 | C2×C3 | semidirect |
| 20. C5×D24 | C2×C3 | semidirect |
| 24. C3×C8×D5 | D3 | semidirect |
| 25. C3×C8×D5 | C2×C3 | semidirect |
| 26. #6654 | C2×C3 | semidirect |
| 38. C3×D24 | D5 | direct (N × H) |
| 42. D60 | C22×C3 | semidirect |
| 43. C5×D12 | C22×C3 | semidirect |
| 51. C3×C5×C8 | C2×D3 | semidirect |
| 52. C3×C5×C8 | C22×C3 | semidirect |
| 54. C3×#168 | C2×D3 | semidirect |
| 55. C3×#168 | C22×C3 | semidirect |
| 61. C32×D5 | D8 | semidirect |
| 66. C8×D5 | C3×D3 | semidirect |
| 71. C3×D12 | C2×D5 | semidirect |
| 73. C32×C8 | C2×D5 | semidirect |
| 99. D24 | C3×D5 | direct (N × H) |
| 100. C32×C5 | C2×D8 | semidirect |
| 106. C5×C8 | C2×C3×D3 | semidirect |
| 107. #168 | C2×C3×D3 | semidirect |
| 122. C3×D5 | D24 | direct (N × H) |
| 123. C3×D5 | C3×D8 | semidirect |
| 135. D12 | C2×C3×D5 | semidirect |
| 140. C3×C8 | D3×D5 | semidirect |
| 141. C3×C8 | C2×C3×D5 | semidirect |
| 158. C3×C5 | C2×D24 | semidirect |
| 159. C3×C5 | C2×C3×D8 | semidirect |
| 178. D5 | C3×D24 | direct (N × H) |
| 179. C32 | D5×D8 | semidirect |
| 186. C8 | C3×D3×D5 | semidirect |
| 197. C5 | C2×C3×D24 | semidirect |
| 205. C3 | D5×D24 | direct (N × H) |
| 206. C3 | C3×D5×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×D12 | 2 |
| C3×D120 | 2 |
| C3×C5×D24 | 2 |
| C32×C8×D5 | 2 |
| C3×#6654 | 2 |
| C3×D5×D8 | 3 |
| D5×D24 | 3 |
| C2×C3×D24 | 5 |