Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
358 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #10623832 | C2 | semidirect |
| 4. #10623828 | C2 | semidirect |
| 7. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 48. C2×C3⋊Dic3 | Dic5 | semidirect |
| 70. C32×C5 | #117 | semidirect |
| 113. C3×C5 | #877 | semidirect |
| 129. C32 | #4072 | semidirect |
| 141. C5 | #63957 | semidirect |
| 149. C3 | #91529 | 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 |
| C3×#6719 | 2 |
| #10623832 | 2 |
| #10623828 | 2 |
| #91529 | 3 |
| #63957 | 5 |