Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
402 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×D3×Dic15 | C2 | semidirect |
| 3. C4⋊(C3⋊Dic15) | C2 | semidirect |
| 4. C3×C4×Dic15 | C2 | semidirect |
| 5. (C2×D3)⋊Dic15 | C2 | semidirect |
| 13. C3×C5×D12 | C4 | semidirect |
| 24. C4×Dic15 | D3 | semidirect |
| 30. C2×C3×C5×D3 | C2×C4 | semidirect |
| 31. C32×C4×C5 | C2×C4 | semidirect |
| 34. C3×Dic15 | D4 | semidirect |
| 53. C5×D12 | Dic3 | semidirect |
| 73. C3×D12 | Dic5 | semidirect |
| 83. C2×C5×D3 | C2×Dic3 | semidirect |
| 85. C3×C4×C5 | C4×D3 | semidirect |
| 86. C3×C4×C5 | C2×Dic3 | semidirect |
| 91. Dic15 | D12 | direct (N × H) |
| 105. C32×C5 | C4×D4 | semidirect |
| 116. C2×C3×D3 | C2×Dic5 | semidirect |
| 117. C32×C4 | C2×Dic5 | semidirect |
| 147. D12 | Dic15 | direct (N × H) |
| 153. C4×C5 | D3×Dic3 | semidirect |
| 167. C3×C5 | C4×D12 | semidirect |
| 168. C3×C5 | D4×Dic3 | semidirect |
| 177. C2×D3 | C2×Dic15 | semidirect |
| 181. C3×C4 | D3×Dic5 | semidirect |
| 182. C3×C4 | C2×Dic15 | semidirect |
| 192. C32 | D4×Dic5 | semidirect |
| 211. C5 | Dic3×D12 | semidirect |
| 219. C4 | D3×Dic15 | semidirect |
| 221. C3 | Dic5×D12 | semidirect |
| 222. C3 | D4×Dic15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D12 | 2 |
| C2×D3×Dic15 | 2 |
| C4⋊(C3⋊Dic15) | 2 |
| C3×C4×Dic15 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| D4×Dic15 | 3 |
| Dic5×D12 | 3 |
| Dic3×D12 | 5 |