Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
108 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 69 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×#168 | C4 | semidirect |
| 18. #3940 | C9 | direct (N × H) |
| 45. C5×C9 | #106 | semidirect |
| 49. #168 | C4×C9 | semidirect |
| 83. C9 | #3940 | direct (N × H) |
| 91. C5 | C9×#106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C9×C4⋊C4 | 2 |
| C9×C4⋊Dic5 | 2 |
| C2×C9×#168 | 2 |
| C3×#3940 | 3 |
| C9×#106 | 5 |