Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
338 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 122 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. Dic3⋊Dic15 | C2 | semidirect |
| 5. Dic3×Dic15 | C2 | semidirect |
| 11. C2×C3×C5×Dic3 | C4 | semidirect |
| 49. C2×C5×Dic3 | Dic3 | semidirect |
| 66. C2×C3×Dic3 | Dic5 | semidirect |
| 98. C32×C5 | #117 | semidirect |
| 133. C2×Dic3 | Dic15 | semidirect |
| 152. C3×C5 | #877 | semidirect |
| 153. C3×C5 | #926 | semidirect |
| 175. C32 | #4072 | semidirect |
| 191. C5 | #63955 | semidirect |
| 200. C3 | #91529 | semidirect |
| 201. C3 | #91815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Dic3 | 2 |
| #10623913 | 2 |
| C3×#6719 | 2 |
| Dic3⋊Dic15 | 2 |
| Dic3×Dic15 | 2 |
| #91815 | 3 |
| #91529 | 3 |
| #63955 | 5 |