Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
228 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 6. C2×C4×C5×C9 | C4 | semidirect |
| 9. C2×C9×Dic5 | C4 | semidirect |
| 20. #3963 | C9 | direct (N × H) |
| 42. C2×C4×C9 | Dic5 | semidirect |
| 52. C5×C9 | #95 | semidirect |
| 55. C2×C4×C5 | C4×C9 | semidirect |
| 58. C2×Dic5 | C4×C9 | semidirect |
| 105. C9 | #3963 | direct (N × H) |
| 111. C2×C4 | C9×Dic5 | semidirect |
| 117. C5 | C9×#95 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×C9 | 2 |
| C22×C9×Dic5 | 2 |
| C3×#3963 | 3 |
| C9×#95 | 5 |