Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
468 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 128 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×C32×Dic5 | C2 | semidirect |
| 3. C5×#3757 | C2 | semidirect |
| 4. #10623775 | C2 | semidirect |
| 5. #10623772 | C2 | semidirect |
| 16. C22×C3×Dic5 | D3 | semidirect |
| 31. #3757 | D5 | semidirect |
| 47. C22×Dic5 | C3⋊D3 | semidirect |
| 71. C32×C5 | #123 | semidirect |
| 116. C3×C5 | #929 | semidirect |
| 129. C32 | #4032 | semidirect |
| 141. C5 | #64138 | semidirect |
| 150. C3 | #91546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67184 | 2 |
| C22×C32×Dic5 | 2 |
| C5×#3757 | 2 |
| #10623775 | 2 |
| #10623772 | 2 |
| #91546 | 3 |
| #64138 | 5 |