Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
358 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×C4⋊Dic15 | C2 | semidirect |
| 3. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 5. Dic3×Dic15 | C2 | semidirect |
| 11. C4×C3⋊D15 | C4 | semidirect |
| 20. C4⋊Dic15 | D3 | semidirect |
| 22. C5×C4⋊Dic3 | D3 | semidirect |
| 37. C3×C4⋊Dic3 | D5 | semidirect |
| 103. C4⋊Dic3 | D15 | semidirect |
| 106. C32×C5 | #117 | semidirect |
| 168. C3×C5 | #892 | semidirect |
| 169. C3×C5 | #892 | semidirect |
| 196. C32 | #4038 | semidirect |
| 215. C5 | #63849 | semidirect |
| 225. C3 | #91347 | semidirect |
| 226. C3 | #91781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊D15 | 2 |
| C3×C4⋊Dic15 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| #10623813 | 2 |
| Dic3×Dic15 | 2 |
| #91781 | 3 |
| #91347 | 3 |
| #63849 | 5 |