Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
126 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 75 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. C5×Q8×C9 | C4 | semidirect |
| 20. #3967 | C9 | direct (N × H) |
| 38. Q8×C9 | Dic5 | semidirect |
| 51. C5×C9 | #103 | semidirect |
| 53. C5×Q8 | C4×C9 | semidirect |
| 93. C9 | #3967 | direct (N × H) |
| 95. Q8 | C9×Dic5 | semidirect |
| 103. C5 | C9×#103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×C9 | 2 |
| C9×C4⋊Dic5 | 2 |
| C2×C9×#168 | 2 |
| C3×#3967 | 3 |
| C9×#103 | 5 |