Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 120 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. C3×C4×C5×Dic3 | C2 | semidirect |
| 3. C32×C4×Dic5 | C2 | semidirect |
| 4. C3×#6669 | C2 | semidirect |
| 7. #91386 | C3 | direct (N × H) |
| 11. C3×C4×D15 | C4 | semidirect |
| 18. C4×C5×Dic3 | C2×C3 | semidirect |
| 22. C3×C4×Dic5 | D3 | semidirect |
| 23. C3×C4×Dic5 | C2×C3 | semidirect |
| 24. #6669 | C2×C3 | semidirect |
| 38. C3×C4×Dic3 | D5 | semidirect |
| 46. C4×D15 | C3×C4 | semidirect |
| 62. C4×Dic5 | C3×D3 | semidirect |
| 96. C4×Dic3 | C3×D5 | semidirect |
| 97. C32×C5 | #117 | semidirect |
| 150. C3×C5 | #872 | semidirect |
| 151. C3×C5 | C3×#117 | semidirect |
| 172. C32 | #4018 | semidirect |
| 187. C5 | C3×#872 | semidirect |
| 196. C3 | #91386 | direct (N × H) |
| 197. C3 | C3×#4018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D15 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C32×C4×Dic5 | 2 |
| C3×#6669 | 2 |
| C3×#6667 | 2 |
| C3×#4018 | 3 |
| #91386 | 3 |
| C3×#872 | 5 |