Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
150 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 150 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 |
|---|---|---|
| 2. C4⋊Dic45 | C2 | semidirect |
| 3. C2×C9⋊#168 | C2 | semidirect |
| 7. C5×D4×C9 | C4 | semidirect |
| 42. D4×C9 | Dic5 | semidirect |
| 56. C5×C9 | #102 | semidirect |
| 59. C5×D4 | Dic9 | semidirect |
| 107. C9 | #3964 | semidirect |
| 110. D4 | Dic45 | semidirect |
| 118. C5 | #63392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C9 | 2 |
| C4⋊Dic45 | 2 |
| C2×C9⋊#168 | 2 |
| #91116 | 3 |
| #63392 | 5 |