Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
294 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×C3×Dic30 | C2 | semidirect |
| 3. C2×C32×#168 | C2 | semidirect |
| 4. C3×#6659 | C2 | direct (N × H) |
| 6. C2×#6659 | C3 | direct (N × H) |
| 11. C3×Dic30 | C22 | semidirect |
| 14. C32×#168 | C22 | semidirect |
| 17. C2×Dic30 | C2×C3 | semidirect |
| 22. C2×C3×#168 | D3 | semidirect |
| 23. C2×C3×#168 | C2×C3 | semidirect |
| 24. #6659 | C2×C3 | direct (N × H) |
| 45. Dic30 | C22×C3 | semidirect |
| 52. C3×#168 | C2×D3 | semidirect |
| 53. C3×#168 | C22×C3 | semidirect |
| 56. C2×C32×C5 | SD16 | semidirect |
| 62. C2×#168 | C3×D3 | semidirect |
| 95. C32×C5 | C2×SD16 | semidirect |
| 103. #168 | C2×C3×D3 | semidirect |
| 114. C2×C3×C5 | #204 | semidirect |
| 115. C2×C3×C5 | C3×SD16 | semidirect |
| 143. C2×C32 | #687 | semidirect |
| 151. C3×C5 | C2×#204 | semidirect |
| 152. C3×C5 | C2×C3×SD16 | semidirect |
| 169. C2×C5 | C3×#204 | semidirect |
| 171. C32 | C2×#687 | semidirect |
| 183. C2×C3 | #6659 | direct (N × H) |
| 184. C2×C3 | C3×#687 | semidirect |
| 188. C5 | C2×C3×#204 | semidirect |
| 196. C3 | C2×#6659 | direct (N × H) |
| 197. C3 | C2×C3×#687 | semidirect |
| 199. C2 | C3×#6659 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic30 | 2 |
| C2×C3×C5×D12 | 2 |
| C2×C32×#168 | 2 |
| C3×#6659 | 2 |
| C2×C3×#687 | 3 |
| C2×#6659 | 3 |
| C2×C3×#204 | 5 |