Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
150 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 67 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×C9⋊#168 | C2 | semidirect |
| 3. C2×C5×C9⋊C8 | C2 | semidirect |
| 19. C2×C9×D5 | C8 | semidirect |
| 26. C2×C9⋊C8 | D5 | semidirect |
| 59. C5×C9 | C22⋊C8 | semidirect |
| 89. C2×D5 | C9⋊C8 | semidirect |
| 112. C9 | #3952 | semidirect |
| 124. C5 | #63389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C9×D5 | 2 |
| C2×C9⋊#168 | 2 |
| C2×C5×C9⋊C8 | 2 |
| #90955 | 3 |
| #63389 | 5 |