Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
366 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. C22×C3×Dic15 | C2 | semidirect |
| 3. C3×#6719 | C2 | semidirect |
| 4. #10623831 | C2 | semidirect |
| 5. #10623830 | C2 | semidirect |
| 16. C22×Dic15 | D3 | semidirect |
| 21. #6719 | D3 | semidirect |
| 110. C32×C5 | #123 | semidirect |
| 175. C3×C5 | #886 | semidirect |
| 176. C3×C5 | #929 | semidirect |
| 203. C32 | #4081 | semidirect |
| 223. C5 | #63966 | semidirect |
| 233. C3 | #91539 | semidirect |
| 234. C3 | #91543 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#638 | 2 |
| C22×C3×Dic15 | 2 |
| C3×#6719 | 2 |
| #10623831 | 2 |
| #10623830 | 2 |
| #91543 | 3 |
| #91539 | 3 |
| #63966 | 5 |