Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
338 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 106 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. #10623814 | C2 | semidirect |
| 5. Dic3×Dic15 | C2 | semidirect |
| 10. C2×C3×Dic15 | C4 | semidirect |
| 46. C2×Dic15 | Dic3 | semidirect |
| 98. C32×C5 | #117 | semidirect |
| 152. C3×C5 | #877 | semidirect |
| 153. C3×C5 | #926 | semidirect |
| 175. C32 | #4023 | semidirect |
| 191. C5 | #63955 | semidirect |
| 200. C3 | #91528 | semidirect |
| 201. C3 | #91766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic15 | 2 |
| #10623913 | 2 |
| C3×C5×#217 | 2 |
| #10623814 | 2 |
| Dic3×Dic15 | 2 |
| #91766 | 3 |
| #91528 | 3 |
| #63955 | 5 |