Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 66 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. D12×D15 | C2 | semidirect |
| 2. #10623901 | C2 | semidirect |
| 3. C3×C8×D15 | C2 | semidirect |
| 4. C3×C5×D24 | C2 | semidirect |
| 5. #10623800 | C2 | semidirect |
| 9. C4⋊(C3⋊D15) | C22 | semidirect |
| 11. C3×C5×D12 | C22 | semidirect |
| 13. C32×C5×C8 | C22 | semidirect |
| 14. C3×C3⋊#168 | C22 | semidirect |
| 23. C8×D15 | D3 | semidirect |
| 24. C5×D24 | D3 | semidirect |
| 36. C3×D24 | D5 | semidirect |
| 47. C5×D12 | C2×D3 | semidirect |
| 51. C3×C5×C8 | C2×D3 | semidirect |
| 52. C3×C5×C8 | C2×D3 | semidirect |
| 53. C3⋊#168 | C2×D3 | semidirect |
| 59. C3×D15 | D8 | semidirect |
| 68. C3×D12 | C2×D5 | semidirect |
| 71. C32×C8 | C2×D5 | semidirect |
| 96. D24 | D15 | direct (N × H) |
| 98. C32×C5 | C2×D8 | semidirect |
| 104. C5×C8 | D32 | semidirect |
| 120. D15 | D24 | direct (N × H) |
| 132. D12 | C2×D15 | semidirect |
| 136. C3×C8 | D3×D5 | semidirect |
| 137. C3×C8 | C2×D15 | semidirect |
| 155. C3×C5 | C2×D24 | semidirect |
| 156. C3×C5 | D3×D8 | semidirect |
| 175. C32 | D5×D8 | semidirect |
| 182. C8 | D3×D15 | semidirect |
| 193. C5 | D3×D24 | semidirect |
| 201. C3 | D5×D24 | semidirect |
| 202. C3 | D8×D15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D12×D15 | 2 |
| #10623901 | 2 |
| C3×C8×D15 | 2 |
| C3×C5×D24 | 2 |
| #10623800 | 2 |
| D8×D15 | 3 |
| D5×D24 | 3 |
| D3×D24 | 5 |