Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 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. C8×D45 | C2 | semidirect |
| 3. C5×C8×D9 | C2 | semidirect |
| 4. C8×C9×D5 | C2 | semidirect |
| 5. #10623547 | C2 | semidirect |
| 6. #10623541 | C2 | semidirect |
| 7. #10623540 | C2 | semidirect |
| 42. C8×D9 | D5 | semidirect |
| 65. C8×D5 | D9 | semidirect |
| 91. C5×C9 | #131 | semidirect |
| 156. C9 | #4047 | semidirect |
| 172. C5 | #63464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623663 | 2 |
| C8×D45 | 2 |
| C5×C8×D9 | 2 |
| C8×C9×D5 | 2 |
| #10623547 | 2 |
| #10623541 | 2 |
| #10623540 | 2 |
| #91265 | 3 |
| #63464 | 5 |