Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. C2×C5×C8×C9 | C2 | semidirect |
| 3. C4⋊Dic45 | C2 | semidirect |
| 9. D180 | C4 | semidirect |
| 24. C2×C8×C9 | D5 | semidirect |
| 38. C2×C5×C8 | D9 | semidirect |
| 56. C5×C9 | #102 | semidirect |
| 93. C2×C8 | D45 | semidirect |
| 107. C9 | #3953 | semidirect |
| 118. C5 | #63380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D180 | 2 |
| C2×C5×C8×C9 | 2 |
| C4⋊Dic45 | 2 |
| #91105 | 3 |
| #63380 | 5 |