Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
306 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 13. C3×C5×Dic6 | C4 | semidirect |
| 30. C3×Dic15 | Q8 | semidirect |
| 49. C5×Dic6 | Dic3 | semidirect |
| 67. C3×Dic6 | Dic5 | semidirect |
| 79. Dic15 | Dic6 | direct (N × H) |
| 94. C32×C5 | C4×Q8 | semidirect |
| 130. Dic6 | Dic15 | direct (N × H) |
| 146. C3×C5 | C4×Dic6 | semidirect |
| 147. C3×C5 | Q8×Dic3 | semidirect |
| 166. C32 | Q8×Dic5 | semidirect |
| 182. C5 | Dic3×Dic6 | semidirect |
| 190. C3 | Dic5×Dic6 | semidirect |
| 191. C3 | Q8×Dic15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Dic6 | 2 |
| C4⋊(C3⋊Dic15) | 2 |
| C3×C4×Dic15 | 2 |
| Dic3⋊Dic15 | 2 |
| Dic3×Dic15 | 2 |
| Q8×Dic15 | 3 |
| Dic5×Dic6 | 3 |
| Dic3×Dic6 | 5 |