Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 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×#6817 | C2 | semidirect |
| 2. C2×C3×C5×D12 | C2 | semidirect |
| 3. C32×#681 | C2 | semidirect |
| 4. C3×#6659 | C2 | semidirect |
| 5. C3×#6654 | C2 | semidirect |
| 7. #91304 | C3 | direct (N × H) |
| 11. C3×D60 | C22 | semidirect |
| 13. C3×Dic30 | C22 | semidirect |
| 16. C32×#168 | C22 | semidirect |
| 19. #6817 | C2×C3 | semidirect |
| 20. C2×C5×D12 | C2×C3 | semidirect |
| 25. C3×#681 | D3 | semidirect |
| 26. C3×#681 | C2×C3 | semidirect |
| 27. #6659 | C2×C3 | semidirect |
| 28. #6654 | C2×C3 | semidirect |
| 38. C2×C3×D12 | D5 | semidirect |
| 50. D60 | C22×C3 | semidirect |
| 52. Dic30 | C22×C3 | semidirect |
| 60. C3×#168 | C2×D3 | semidirect |
| 61. C3×#168 | C22×C3 | semidirect |
| 72. #681 | C3×D3 | semidirect |
| 102. C2×D12 | C3×D5 | semidirect |
| 110. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 119. #168 | C2×C3×D3 | semidirect |
| 175. C3×C5 | #908 | semidirect |
| 176. C3×C5 | C3×AGL(1,ℤ/8) | semidirect |
| 198. C32 | #4078 | semidirect |
| 218. C5 | C3×#908 | semidirect |
| 227. C3 | #91304 | direct (N × H) |
| 228. C3 | C3×#4078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6817 | 2 |
| C2×C3×C5×D12 | 2 |
| C32×#681 | 2 |
| C3×#6659 | 2 |
| C3×#6654 | 2 |
| C3×#4078 | 3 |
| #91304 | 3 |
| C3×#908 | 5 |