Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
338 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 126 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. C3×#6712 | C2 | semidirect |
| 5. C3×C4×Dic15 | C2 | semidirect |
| 6. #91766 | C3 | direct (N × H) |
| 10. C2×C3×Dic15 | C4 | semidirect |
| 21. #6712 | C2×C3 | semidirect |
| 22. C4×Dic15 | C2×C3 | semidirect |
| 45. C2×Dic15 | C3×C4 | semidirect |
| 98. C32×C5 | #117 | semidirect |
| 152. C3×C5 | #877 | semidirect |
| 153. C3×C5 | C3×#117 | semidirect |
| 175. C32 | #4023 | semidirect |
| 191. C5 | C3×#877 | semidirect |
| 200. C3 | C3×#4023 | semidirect |
| 201. C3 | #91766 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic15 | 2 |
| C32×C5×C22⋊C4 | 2 |
| C3×#6719 | 2 |
| C3×#6712 | 2 |
| C3×C4×Dic15 | 2 |
| #91766 | 3 |
| C3×#4023 | 3 |
| C3×#877 | 5 |