Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 63 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. #10624222 | C2 | semidirect |
| 3. C3×#6716 | C2 | semidirect |
| 4. #10623824 | C2 | semidirect |
| 5. #10623818 | C2 | semidirect |
| 12. C3×Dic30 | C22 | semidirect |
| 15. C3×C3⋊#168 | C22 | semidirect |
| 20. #6716 | D3 | semidirect |
| 42. Dic30 | C2×D3 | semidirect |
| 52. C3⋊#168 | C2×D3 | semidirect |
| 58. C5×C3⋊D3 | SD16 | semidirect |
| 95. C32×C5 | C2×SD16 | semidirect |
| 147. C3⋊D3 | #687 | semidirect |
| 154. C3×C5 | D3×SD16 | semidirect |
| 173. C32 | C2×#687 | semidirect |
| 191. C5 | #63930 | semidirect |
| 200. C3 | D3×#687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×C3⋊D3 | 2 |
| #10624222 | 2 |
| C3×#6716 | 2 |
| #10623824 | 2 |
| #10623818 | 2 |
| D3×#687 | 3 |
| #63930 | 5 |