Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
410 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 100 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×#67149 | C2 | semidirect |
| 3. C2×Dic3×D15 | C2 | semidirect |
| 4. #10623908 | C2 | semidirect |
| 5. C3×#6714 | C2 | semidirect |
| 6. C3×C4×C5×Dic3 | C2 | semidirect |
| 7. Dic3⋊Dic15 | C2 | semidirect |
| 17. #67151 | C4 | semidirect |
| 31. #6714 | D3 | semidirect |
| 33. C4×C5×Dic3 | D3 | semidirect |
| 39. C2×C3⋊D15 | C2×C4 | semidirect |
| 42. C2×C3×D15 | C2×C4 | semidirect |
| 46. C3×C5×Dic3 | C2×C4 | semidirect |
| 47. C3×C5×Dic3 | D4 | semidirect |
| 54. C3×C4×Dic3 | D5 | semidirect |
| 117. C2×D15 | C4×D3 | semidirect |
| 131. C5×Dic3 | C4×D3 | semidirect |
| 132. C5×Dic3 | D12 | semidirect |
| 147. C4×Dic3 | D15 | semidirect |
| 148. C32×C5 | C4×D4 | semidirect |
| 169. C3×Dic3 | C4×D5 | semidirect |
| 170. C3×Dic3 | D20 | semidirect |
| 234. C3×C5 | C4×D12 | semidirect |
| 235. C3×C5 | #67⋊C4 | semidirect |
| 264. Dic3 | C4×D15 | semidirect |
| 265. Dic3 | D60 | semidirect |
| 271. C32 | C4×D20 | semidirect |
| 296. C5 | #63880 | semidirect |
| 310. C3 | #91395 | semidirect |
| 311. C3 | C4×D60 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67151 | 2 |
| C2×#67149 | 2 |
| C2×Dic3×D15 | 2 |
| #10623908 | 2 |
| C3×#6714 | 2 |
| C3×C4×C5×Dic3 | 2 |
| Dic3⋊Dic15 | 2 |
| C4×D60 | 3 |
| #91395 | 3 |
| #63880 | 5 |