Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 108 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. C2×#67141 | C2 | semidirect |
| 3. #10623913 | C2 | semidirect |
| 4. C32×C22⋊Dic5 | C2 | semidirect |
| 5. #10623771 | C2 | semidirect |
| 6. #10623771 | C2 | semidirect |
| 7. Dic5×C3⋊Dic3 | C2 | semidirect |
| 22. C3×C22⋊Dic5 | D3 | semidirect |
| 66. C22⋊Dic5 | C3⋊D3 | semidirect |
| 96. C32×C5 | #124 | semidirect |
| 157. C3×C5 | #885 | semidirect |
| 175. C32 | #4082 | semidirect |
| 190. C5 | #64094 | semidirect |
| 203. C3 | #91525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#638 | 2 |
| C2×#67141 | 2 |
| #10623913 | 2 |
| C32×C22⋊Dic5 | 2 |
| #10623771 | 2 |
| Dic5×C3⋊Dic3 | 2 |
| #91525 | 3 |
| #64094 | 5 |