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 |
|---|---|---|
| 1. C22×C5×C3⋊Dic3 | C2 | semidirect |
| 3. C3×#6719 | C2 | semidirect |
| 4. #10623831 | C2 | semidirect |
| 5. #10623829 | C2 | semidirect |
| 21. #6719 | D3 | semidirect |
| 36. C22×C3⋊Dic3 | D5 | semidirect |
| 107. C32×C5 | #123 | semidirect |
| 170. C3×C5 | #886 | semidirect |
| 171. C3×C5 | #935 | semidirect |
| 196. C32 | #4075 | semidirect |
| 215. C5 | #63962 | semidirect |
| 225. C3 | #91536 | semidirect |
| 226. C3 | #91542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C2×C3×#1220 | 2 |
| C3×#6719 | 2 |
| #10623831 | 2 |
| #10623829 | 2 |
| #91542 | 3 |
| #91536 | 3 |
| #63962 | 5 |