| extension | φ:Q→Aut N | d | ρ | Label | ID |
|---|
| C6.1S3≀C2 = He3⋊2SD16 | φ: S3≀C2/C32⋊C4 → C2 ⊆ Aut C6 | 72 | 6 | C6.1S3wrC2 | 432,234 |
| C6.2S3≀C2 = He3⋊D8 | φ: S3≀C2/C32⋊C4 → C2 ⊆ Aut C6 | 72 | 6+ | C6.2S3wrC2 | 432,235 |
| C6.3S3≀C2 = He3⋊Q16 | φ: S3≀C2/C32⋊C4 → C2 ⊆ Aut C6 | 144 | 6- | C6.3S3wrC2 | 432,236 |
| C6.4S3≀C2 = C6.S3≀C2 | φ: S3≀C2/C32⋊C4 → C2 ⊆ Aut C6 | 72 | 6- | C6.4S3wrC2 | 432,237 |
| C6.5S3≀C2 = C32⋊D6⋊C4 | φ: S3≀C2/C32⋊C4 → C2 ⊆ Aut C6 | 36 | 6 | C6.5S3wrC2 | 432,238 |
| C6.6S3≀C2 = C2×He3⋊D4 | φ: S3≀C2/C32⋊C4 → C2 ⊆ Aut C6 | 36 | 6+ | C6.6S3wrC2 | 432,530 |
| C6.7S3≀C2 = (C3×C6).8D12 | φ: S3≀C2/C32⋊C4 → C2 ⊆ Aut C6 | 24 | 8+ | C6.7S3wrC2 | 432,586 |
| C6.8S3≀C2 = (C3×C6).9D12 | φ: S3≀C2/C32⋊C4 → C2 ⊆ Aut C6 | 48 | 8- | C6.8S3wrC2 | 432,587 |
| C6.9S3≀C2 = C32⋊2D24 | φ: S3≀C2/C32⋊C4 → C2 ⊆ Aut C6 | 24 | 8+ | C6.9S3wrC2 | 432,588 |
| C6.10S3≀C2 = C33⋊8SD16 | φ: S3≀C2/C32⋊C4 → C2 ⊆ Aut C6 | 24 | 8+ | C6.10S3wrC2 | 432,589 |
| C6.11S3≀C2 = C33⋊3Q16 | φ: S3≀C2/C32⋊C4 → C2 ⊆ Aut C6 | 48 | 8- | C6.11S3wrC2 | 432,590 |
| C6.12S3≀C2 = C3⋊S3.2D12 | φ: S3≀C2/S32 → C2 ⊆ Aut C6 | 24 | 4 | C6.12S3wrC2 | 432,579 |
| C6.13S3≀C2 = S32⋊Dic3 | φ: S3≀C2/S32 → C2 ⊆ Aut C6 | 24 | 4 | C6.13S3wrC2 | 432,580 |
| C6.14S3≀C2 = C33⋊C4⋊C4 | φ: S3≀C2/S32 → C2 ⊆ Aut C6 | 48 | 4 | C6.14S3wrC2 | 432,581 |
| C6.15S3≀C2 = C33⋊D8 | φ: S3≀C2/S32 → C2 ⊆ Aut C6 | 24 | 4 | C6.15S3wrC2 | 432,582 |
| C6.16S3≀C2 = C33⋊6SD16 | φ: S3≀C2/S32 → C2 ⊆ Aut C6 | 24 | 4 | C6.16S3wrC2 | 432,583 |
| C6.17S3≀C2 = C33⋊7SD16 | φ: S3≀C2/S32 → C2 ⊆ Aut C6 | 24 | 4 | C6.17S3wrC2 | 432,584 |
| C6.18S3≀C2 = C33⋊Q16 | φ: S3≀C2/S32 → C2 ⊆ Aut C6 | 48 | 4 | C6.18S3wrC2 | 432,585 |
| C6.19S3≀C2 = C3×S32⋊C4 | central extension (φ=1) | 24 | 4 | C6.19S3wrC2 | 432,574 |
| C6.20S3≀C2 = C3×C3⋊S3.Q8 | central extension (φ=1) | 48 | 4 | C6.20S3wrC2 | 432,575 |
| C6.21S3≀C2 = C3×C32⋊D8 | central extension (φ=1) | 24 | 4 | C6.21S3wrC2 | 432,576 |
| C6.22S3≀C2 = C3×C32⋊2SD16 | central extension (φ=1) | 24 | 4 | C6.22S3wrC2 | 432,577 |
| C6.23S3≀C2 = C3×C32⋊Q16 | central extension (φ=1) | 48 | 4 | C6.23S3wrC2 | 432,578 |