Template:Groups of order 56 table
| Group | Second part of GAP ID | Abelian | Nilpotent | Direct Product |
|---|---|---|---|---|
| Nontrivial semidirect product of Z7 and Z8 | 1 | no | no | no |
| Cyclic group:Z56 | 2 | yes | yes | no |
| Dicyclic group:Dic56 | 3 | no | no | no |
| Direct product of Z4 and D14 | 4 | no | no | yes |
| Dihedral group:D56 | 5 | no | no | no |
| Direct product of Z2 and Dic28 | 6 | no | no | yes |
| Nontrivial semidirect product of Z7 and D8 | 7 | no | no | no |
| Direct product of Z2 and Z28 | 8 | yes | yes | yes |
| Direct product of Z7 and D8 | 9 | no | yes | yes |
| Direct product of Z7 and Q8 | 10 | no | yes | yes |
| General affine group:GA(1,8) | 11 | no | no | no |
| Direct product of V4 and D14 | 12 | no | no | yes |
| Direct product of V4 and Z14 | 13 | yes | yes | yes |