| extension | φ:Q→Aut N | d | ρ | Label | ID |
| C6.1(C4×S3) = C12.29D6 | φ: C4×S3/Dic3 → C2 ⊆ Aut C6 | 24 | 4 | C6.1(C4xS3) | 144,53 |
| C6.2(C4×S3) = C12.31D6 | φ: C4×S3/Dic3 → C2 ⊆ Aut C6 | 24 | 4 | C6.2(C4xS3) | 144,55 |
| C6.3(C4×S3) = C6.D12 | φ: C4×S3/Dic3 → C2 ⊆ Aut C6 | 24 | | C6.3(C4xS3) | 144,65 |
| C6.4(C4×S3) = C62.C22 | φ: C4×S3/Dic3 → C2 ⊆ Aut C6 | 48 | | C6.4(C4xS3) | 144,67 |
| C6.5(C4×S3) = C8×D9 | φ: C4×S3/C12 → C2 ⊆ Aut C6 | 72 | 2 | C6.5(C4xS3) | 144,5 |
| C6.6(C4×S3) = C8⋊D9 | φ: C4×S3/C12 → C2 ⊆ Aut C6 | 72 | 2 | C6.6(C4xS3) | 144,6 |
| C6.7(C4×S3) = C4×Dic9 | φ: C4×S3/C12 → C2 ⊆ Aut C6 | 144 | | C6.7(C4xS3) | 144,11 |
| C6.8(C4×S3) = Dic9⋊C4 | φ: C4×S3/C12 → C2 ⊆ Aut C6 | 144 | | C6.8(C4xS3) | 144,12 |
| C6.9(C4×S3) = D18⋊C4 | φ: C4×S3/C12 → C2 ⊆ Aut C6 | 72 | | C6.9(C4xS3) | 144,14 |
| C6.10(C4×S3) = C2×C4×D9 | φ: C4×S3/C12 → C2 ⊆ Aut C6 | 72 | | C6.10(C4xS3) | 144,38 |
| C6.11(C4×S3) = C8×C3⋊S3 | φ: C4×S3/C12 → C2 ⊆ Aut C6 | 72 | | C6.11(C4xS3) | 144,85 |
| C6.12(C4×S3) = C24⋊S3 | φ: C4×S3/C12 → C2 ⊆ Aut C6 | 72 | | C6.12(C4xS3) | 144,86 |
| C6.13(C4×S3) = C4×C3⋊Dic3 | φ: C4×S3/C12 → C2 ⊆ Aut C6 | 144 | | C6.13(C4xS3) | 144,92 |
| C6.14(C4×S3) = C6.Dic6 | φ: C4×S3/C12 → C2 ⊆ Aut C6 | 144 | | C6.14(C4xS3) | 144,93 |
| C6.15(C4×S3) = C6.11D12 | φ: C4×S3/C12 → C2 ⊆ Aut C6 | 72 | | C6.15(C4xS3) | 144,95 |
| C6.16(C4×S3) = S3×C3⋊C8 | φ: C4×S3/D6 → C2 ⊆ Aut C6 | 48 | 4 | C6.16(C4xS3) | 144,52 |
| C6.17(C4×S3) = D6.Dic3 | φ: C4×S3/D6 → C2 ⊆ Aut C6 | 48 | 4 | C6.17(C4xS3) | 144,54 |
| C6.18(C4×S3) = Dic32 | φ: C4×S3/D6 → C2 ⊆ Aut C6 | 48 | | C6.18(C4xS3) | 144,63 |
| C6.19(C4×S3) = D6⋊Dic3 | φ: C4×S3/D6 → C2 ⊆ Aut C6 | 48 | | C6.19(C4xS3) | 144,64 |
| C6.20(C4×S3) = Dic3⋊Dic3 | φ: C4×S3/D6 → C2 ⊆ Aut C6 | 48 | | C6.20(C4xS3) | 144,66 |
| C6.21(C4×S3) = S3×C24 | central extension (φ=1) | 48 | 2 | C6.21(C4xS3) | 144,69 |
| C6.22(C4×S3) = C3×C8⋊S3 | central extension (φ=1) | 48 | 2 | C6.22(C4xS3) | 144,70 |
| C6.23(C4×S3) = Dic3×C12 | central extension (φ=1) | 48 | | C6.23(C4xS3) | 144,76 |
| C6.24(C4×S3) = C3×Dic3⋊C4 | central extension (φ=1) | 48 | | C6.24(C4xS3) | 144,77 |
| C6.25(C4×S3) = C3×D6⋊C4 | central extension (φ=1) | 48 | | C6.25(C4xS3) | 144,79 |