Direct product G=N×Q with N=C23 and Q=S4
Semidirect products G=N:Q with N=C23 and Q=S4
Non-split extensions G=N.Q with N=C23 and Q=S4
| extension | φ:Q→Aut N | d | ρ | Label | ID |
|---|
| C23.1S4 = C24⋊Dic3 | φ: S4/C1 → S4 ⊆ Aut C23 | 16 | 12+ | C2^3.1S4 | 192,184 |
| C23.2S4 = C42⋊Dic3 | φ: S4/C1 → S4 ⊆ Aut C23 | 16 | 12+ | C2^3.2S4 | 192,185 |
| C23.3S4 = C42⋊D6 | φ: S4/C1 → S4 ⊆ Aut C23 | 12 | 6+ | C2^3.3S4 | 192,956 |
| C23.4S4 = C23.S4 | φ: S4/C1 → S4 ⊆ Aut C23 | 16 | 4 | C2^3.4S4 | 192,1491 |
| C23.5S4 = Q8.S4 | φ: S4/C1 → S4 ⊆ Aut C23 | 16 | 4 | C2^3.5S4 | 192,1492 |
| C23.6S4 = Q8⋊2S4 | φ: S4/C1 → S4 ⊆ Aut C23 | 8 | 4+ | C2^3.6S4 | 192,1494 |
| C23.7S4 = C23.7S4 | φ: S4/C22 → S3 ⊆ Aut C23 | 24 | 6 | C2^3.7S4 | 192,180 |
| C23.8S4 = C23.8S4 | φ: S4/C22 → S3 ⊆ Aut C23 | 24 | 6+ | C2^3.8S4 | 192,181 |
| C23.9S4 = C23.9S4 | φ: S4/C22 → S3 ⊆ Aut C23 | 12 | 3 | C2^3.9S4 | 192,182 |
| C23.10S4 = C2×C42⋊S3 | φ: S4/C22 → S3 ⊆ Aut C23 | 12 | 3 | C2^3.10S4 | 192,944 |
| C23.11S4 = Q8.1S4 | φ: S4/C22 → S3 ⊆ Aut C23 | 48 | 6- | C2^3.11S4 | 192,1489 |
| C23.12S4 = Q8⋊S4 | φ: S4/C22 → S3 ⊆ Aut C23 | 24 | 6 | C2^3.12S4 | 192,1490 |
| C23.13S4 = C24⋊4Dic3 | φ: S4/C22 → S3 ⊆ Aut C23 | 12 | 6+ | C2^3.13S4 | 192,1495 |
| C23.14S4 = C23.14S4 | φ: S4/A4 → C2 ⊆ Aut C23 | 32 | | C2^3.14S4 | 192,978 |
| C23.15S4 = C23.15S4 | φ: S4/A4 → C2 ⊆ Aut C23 | 32 | | C2^3.15S4 | 192,979 |
| C23.16S4 = C23.16S4 | φ: S4/A4 → C2 ⊆ Aut C23 | 32 | | C2^3.16S4 | 192,980 |
| C23.17S4 = C25.S3 | φ: S4/A4 → C2 ⊆ Aut C23 | 24 | | C2^3.17S4 | 192,991 |
| C23.18S4 = C2×Q8.D6 | φ: S4/A4 → C2 ⊆ Aut C23 | 32 | | C2^3.18S4 | 192,1476 |
| C23.19S4 = C2×Q8⋊Dic3 | central extension (φ=1) | 64 | | C2^3.19S4 | 192,977 |
| C23.20S4 = C22×CSU2(𝔽3) | central extension (φ=1) | 64 | | C2^3.20S4 | 192,1474 |
| C23.21S4 = C22×GL2(𝔽3) | central extension (φ=1) | 32 | | C2^3.21S4 | 192,1475 |
| C23.22S4 = C22×A4⋊C4 | central extension (φ=1) | 48 | | C2^3.22S4 | 192,1487 |
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