Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
132 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 8. C9⋊#170 | C4 | semidirect |
| 9. C9×#170 | C4 | semidirect |
| 15. Dic45 | C8 | semidirect |
| 18. C5×Dic9 | C8 | semidirect |
| 48. C5×C9 | C4×C8 | semidirect |
| 53. #170 | Dic9 | direct (N × H) |
| 58. Dic9 | #170 | direct (N × H) |
| 88. C9 | C4×#170 | semidirect |
| 97. C5 | C8×Dic9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9⋊#170 | 2 |
| C2×C9×#170 | 2 |
| Dic5×Dic9 | 2 |
| Dic3×#170 | 3 |
| C8×Dic9 | 5 |