| d | ρ | Label | ID | ||
|---|---|---|---|---|---|
| C22×D31 | 124 | C2^2xD31 | 248,11 |
| extension | φ:Q→Aut N | d | ρ | Label | ID |
|---|---|---|---|---|---|
| C2.1D62 = C4×D31 | central extension (φ=1) | 124 | 2 | C2.1D62 | 248,4 |
| C2.2D62 = C2×Dic31 | central extension (φ=1) | 248 | C2.2D62 | 248,6 | |
| C2.3D62 = Dic62 | central stem extension (φ=1) | 248 | 2- | C2.3D62 | 248,3 |
| C2.4D62 = D124 | central stem extension (φ=1) | 124 | 2+ | C2.4D62 | 248,5 |
| C2.5D62 = C31⋊D4 | central stem extension (φ=1) | 124 | 2 | C2.5D62 | 248,7 |