| extension | φ:Q→Aut N | d | ρ | Label | ID |
| C6.1(C2×C32⋊C4) = Dic3×C32⋊C4 | φ: C2×C32⋊C4/C32⋊C4 → C2 ⊆ Aut C6 | 48 | 8- | C6.1(C2xC3^2:C4) | 432,567 |
| C6.2(C2×C32⋊C4) = D6⋊(C32⋊C4) | φ: C2×C32⋊C4/C32⋊C4 → C2 ⊆ Aut C6 | 24 | 8+ | C6.2(C2xC3^2:C4) | 432,568 |
| C6.3(C2×C32⋊C4) = C33⋊(C4⋊C4) | φ: C2×C32⋊C4/C32⋊C4 → C2 ⊆ Aut C6 | 48 | 8- | C6.3(C2xC3^2:C4) | 432,569 |
| C6.4(C2×C32⋊C4) = S3×C32⋊2C8 | φ: C2×C32⋊C4/C32⋊C4 → C2 ⊆ Aut C6 | 48 | 8- | C6.4(C2xC3^2:C4) | 432,570 |
| C6.5(C2×C32⋊C4) = C33⋊5(C2×C8) | φ: C2×C32⋊C4/C32⋊C4 → C2 ⊆ Aut C6 | 24 | 8+ | C6.5(C2xC3^2:C4) | 432,571 |
| C6.6(C2×C32⋊C4) = C33⋊M4(2) | φ: C2×C32⋊C4/C32⋊C4 → C2 ⊆ Aut C6 | 48 | 8- | C6.6(C2xC3^2:C4) | 432,572 |
| C6.7(C2×C32⋊C4) = C33⋊2M4(2) | φ: C2×C32⋊C4/C32⋊C4 → C2 ⊆ Aut C6 | 24 | 8+ | C6.7(C2xC3^2:C4) | 432,573 |
| C6.8(C2×C32⋊C4) = C33⋊7(C2×C8) | φ: C2×C32⋊C4/C2×C3⋊S3 → C2 ⊆ Aut C6 | 48 | 4 | C6.8(C2xC3^2:C4) | 432,635 |
| C6.9(C2×C32⋊C4) = C33⋊4M4(2) | φ: C2×C32⋊C4/C2×C3⋊S3 → C2 ⊆ Aut C6 | 48 | 4 | C6.9(C2xC3^2:C4) | 432,636 |
| C6.10(C2×C32⋊C4) = C4×C33⋊C4 | φ: C2×C32⋊C4/C2×C3⋊S3 → C2 ⊆ Aut C6 | 48 | 4 | C6.10(C2xC3^2:C4) | 432,637 |
| C6.11(C2×C32⋊C4) = C33⋊9(C4⋊C4) | φ: C2×C32⋊C4/C2×C3⋊S3 → C2 ⊆ Aut C6 | 48 | 4 | C6.11(C2xC3^2:C4) | 432,638 |
| C6.12(C2×C32⋊C4) = C2×C33⋊4C8 | φ: C2×C32⋊C4/C2×C3⋊S3 → C2 ⊆ Aut C6 | 48 | | C6.12(C2xC3^2:C4) | 432,639 |
| C6.13(C2×C32⋊C4) = C33⋊12M4(2) | φ: C2×C32⋊C4/C2×C3⋊S3 → C2 ⊆ Aut C6 | 24 | 4 | C6.13(C2xC3^2:C4) | 432,640 |
| C6.14(C2×C32⋊C4) = C62⋊11Dic3 | φ: C2×C32⋊C4/C2×C3⋊S3 → C2 ⊆ Aut C6 | 24 | 4 | C6.14(C2xC3^2:C4) | 432,641 |
| C6.15(C2×C32⋊C4) = He3⋊2(C2×C8) | central extension (φ=1) | 72 | 3 | C6.15(C2xC3^2:C4) | 432,273 |
| C6.16(C2×C32⋊C4) = C4×He3⋊C4 | central extension (φ=1) | 72 | 3 | C6.16(C2xC3^2:C4) | 432,275 |
| C6.17(C2×C32⋊C4) = C2×He3⋊2C8 | central extension (φ=1) | 144 | | C6.17(C2xC3^2:C4) | 432,277 |
| C6.18(C2×C32⋊C4) = C22×He3⋊C4 | central extension (φ=1) | 72 | | C6.18(C2xC3^2:C4) | 432,543 |
| C6.19(C2×C32⋊C4) = C3×C3⋊S3⋊3C8 | central extension (φ=1) | 48 | 4 | C6.19(C2xC3^2:C4) | 432,628 |
| C6.20(C2×C32⋊C4) = C3×C32⋊M4(2) | central extension (φ=1) | 48 | 4 | C6.20(C2xC3^2:C4) | 432,629 |
| C6.21(C2×C32⋊C4) = C12×C32⋊C4 | central extension (φ=1) | 48 | 4 | C6.21(C2xC3^2:C4) | 432,630 |
| C6.22(C2×C32⋊C4) = C3×C4⋊(C32⋊C4) | central extension (φ=1) | 48 | 4 | C6.22(C2xC3^2:C4) | 432,631 |
| C6.23(C2×C32⋊C4) = C6×C32⋊2C8 | central extension (φ=1) | 48 | | C6.23(C2xC3^2:C4) | 432,632 |
| C6.24(C2×C32⋊C4) = C3×C62.C4 | central extension (φ=1) | 24 | 4 | C6.24(C2xC3^2:C4) | 432,633 |
| C6.25(C2×C32⋊C4) = C3×C62⋊C4 | central extension (φ=1) | 24 | 4 | C6.25(C2xC3^2:C4) | 432,634 |
| C6.26(C2×C32⋊C4) = He3⋊1M4(2) | central stem extension (φ=1) | 72 | 6 | C6.26(C2xC3^2:C4) | 432,274 |
| C6.27(C2×C32⋊C4) = C4⋊(He3⋊C4) | central stem extension (φ=1) | 72 | 6 | C6.27(C2xC3^2:C4) | 432,276 |
| C6.28(C2×C32⋊C4) = He3⋊4M4(2) | central stem extension (φ=1) | 72 | 6 | C6.28(C2xC3^2:C4) | 432,278 |
| C6.29(C2×C32⋊C4) = C22⋊(He3⋊C4) | central stem extension (φ=1) | 36 | 6 | C6.29(C2xC3^2:C4) | 432,279 |