Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
150 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 52 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⋊#170 | C2 | semidirect |
| 3. C2×C9×#170 | C2 | semidirect |
| 19. C2×C5×D9 | C8 | semidirect |
| 41. C2×#170 | D9 | semidirect |
| 59. C5×C9 | C22⋊C8 | semidirect |
| 70. C2×D9 | #170 | semidirect |
| 112. C9 | C22⋊#170 | semidirect |
| 124. C5 | (C2×D9)⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D9×Dic5 | 2 |
| C2×C9⋊#170 | 2 |
| C2×C9×#170 | 2 |
| (C2×D3)⋊#170 | 3 |
| (C2×D9)⋊C8 | 5 |