Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
708 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 213 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. C23×D45 | C2 | semidirect |
| 2. C22×C4×C5×C9 | C2 | semidirect |
| 3. C2×D180 | C2 | direct (N × H) |
| 7. C22×D45 | C22 | semidirect |
| 8. C2×C4×C5×C9 | C22 | semidirect |
| 9. D180 | C22 | direct (N × H) |
| 14. C22×C5×C9 | D4 | semidirect |
| 17. C2×D45 | C23 | semidirect |
| 18. C4×C5×C9 | C23 | semidirect |
| 21. C22×C4×C9 | D5 | semidirect |
| 29. C2×C5×C9 | C2×D4 | semidirect |
| 33. C22×C4×C5 | D9 | semidirect |
| 38. C2×C4×C9 | C2×D5 | semidirect |
| 48. C5×C9 | C22×D4 | semidirect |
| 52. C2×C4×C5 | C2×D9 | semidirect |
| 54. C22×C9 | D20 | semidirect |
| 58. C4×C9 | C22×D5 | semidirect |
| 68. C22×C5 | D36 | semidirect |
| 72. C4×C5 | C22×D9 | semidirect |
| 73. C2×C9 | C2×D20 | semidirect |
| 78. C22×C4 | D45 | semidirect |
| 85. C2×C5 | C2×D36 | semidirect |
| 88. C9 | C22×D20 | semidirect |
| 93. C2×C4 | C2×D45 | semidirect |
| 97. C5 | C22×D36 | semidirect |
| 100. C22 | D180 | direct (N × H) |
| 102. C4 | C22×D45 | semidirect |
| 105. C2 | C2×D180 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D45 | 2 |
| C22×C4×C5×C9 | 2 |
| C2×D180 | 2 |
| C22×D60 | 3 |
| C22×D36 | 5 |