Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 246 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 |
|---|---|---|
| 4. C32×#683 | C2 | semidirect |
| 5. C32×C4×Dic5 | C2 | semidirect |
| 6. C3×#4023 | C3 | direct (N × H) |
| 9. C2×C32×Dic5 | C4 | semidirect |
| 17. C3×#683 | C2×C3 | semidirect |
| 18. C3×C4×Dic5 | C2×C3 | semidirect |
| 26. #4023 | C32 | direct (N × H) |
| 34. C2×C3×Dic5 | C3×C4 | semidirect |
| 45. #683 | C2×C32 | semidirect |
| 46. C4×Dic5 | C2×C32 | semidirect |
| 65. C32×C5 | #117 | semidirect |
| 68. C2×Dic5 | C32×C4 | semidirect |
| 104. C3×C5 | C3×#117 | semidirect |
| 115. C32 | #4023 | direct (N × H) |
| 125. C5 | C32×#117 | semidirect |
| 133. C3 | C3×#4023 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Dic5 | 2 |
| C32×C5×C22⋊C4 | 2 |
| C32×C22⋊Dic5 | 2 |
| C32×#683 | 2 |
| C32×C4×Dic5 | 2 |
| C3×#4023 | 3 |
| C32×#117 | 5 |