| d | ρ | Label | ID | ||
|---|---|---|---|---|---|
| C23×C3⋊Dic3 | 288 | C2^3xC3:Dic3 | 288,1016 |
| extension | φ:Q→Aut N | d | ρ | Label | ID |
|---|---|---|---|---|---|
| C23⋊(C3⋊Dic3) = C2×C6.7S4 | φ: C3⋊Dic3/C6 → S3 ⊆ Aut C23 | 72 | C2^3:(C3:Dic3) | 288,916 | |
| C23⋊2(C3⋊Dic3) = C62.38D4 | φ: C3⋊Dic3/C32 → C4 ⊆ Aut C23 | 72 | C2^3:2(C3:Dic3) | 288,309 | |
| C23⋊3(C3⋊Dic3) = C2×C62⋊5C4 | φ: C3⋊Dic3/C3×C6 → C2 ⊆ Aut C23 | 144 | C2^3:3(C3:Dic3) | 288,809 |
| extension | φ:Q→Aut N | d | ρ | Label | ID |
|---|---|---|---|---|---|
| C23.(C3⋊Dic3) = C12.12S4 | φ: C3⋊Dic3/C6 → S3 ⊆ Aut C23 | 72 | 6 | C2^3.(C3:Dic3) | 288,402 |
| C23.2(C3⋊Dic3) = (C6×D4).S3 | φ: C3⋊Dic3/C32 → C4 ⊆ Aut C23 | 72 | C2^3.2(C3:Dic3) | 288,308 | |
| C23.3(C3⋊Dic3) = C62⋊7C8 | φ: C3⋊Dic3/C3×C6 → C2 ⊆ Aut C23 | 144 | C2^3.3(C3:Dic3) | 288,305 | |
| C23.4(C3⋊Dic3) = C2×C12.58D6 | φ: C3⋊Dic3/C3×C6 → C2 ⊆ Aut C23 | 144 | C2^3.4(C3:Dic3) | 288,778 | |
| C23.5(C3⋊Dic3) = C22×C32⋊4C8 | central extension (φ=1) | 288 | C2^3.5(C3:Dic3) | 288,777 |