Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
492 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C22×C4×C5×C9 | C2 | semidirect |
| 2. C2×#67099 | C2 | semidirect |
| 3. #10623709 | C2 | direct (N × H) |
| 4. C2×D180 | C2 | semidirect |
| 5. C2×C4×D45 | C2 | semidirect |
| 6. C2×Dic90 | C2 | semidirect |
| 12. C2×C4×C5×C9 | C22 | semidirect |
| 13. #67099 | C22 | semidirect |
| 15. D180 | C22 | semidirect |
| 16. C4×D45 | C22 | semidirect |
| 17. Dic90 | C22 | semidirect |
| 34. C22×C4×C9 | D5 | semidirect |
| 52. C2×C5×C9 | #41 | semidirect |
| 55. C22×C4×C5 | D9 | semidirect |
| 65. C2×C4×C9 | C2×D5 | semidirect |
| 85. C5×C9 | C2×#41 | semidirect |
| 90. C2×C4×C5 | C2×D9 | semidirect |
| 128. C2×C9 | #709 | semidirect |
| 136. C22×C4 | D45 | semidirect |
| 147. C2×C5 | #3697 | semidirect |
| 150. C9 | C2×#709 | semidirect |
| 160. C2×C4 | C2×D45 | semidirect |
| 165. C5 | C2×#3697 | semidirect |
| 177. C2 | #10623709 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×C9 | 2 |
| C2×#67099 | 2 |
| #10623709 | 2 |
| C2×D180 | 2 |
| C2×C4×D45 | 2 |
| C2×Dic90 | 2 |
| C2×#6817 | 3 |
| C2×#3697 | 5 |