| d | ρ | Label | ID | ||
|---|---|---|---|---|---|
| C24×C3⋊S3 | 144 | C2^4xC3:S3 | 288,1044 |
| extension | φ:Q→Aut N | d | ρ | Label | ID |
|---|---|---|---|---|---|
| C24⋊(C3⋊S3) = PSO4+ (𝔽3) | φ: C3⋊S3/C1 → C3⋊S3 ⊆ Aut C24 | 12 | 9+ | C2^4:(C3:S3) | 288,1026 |
| C24⋊2(C3⋊S3) = (C2×C6)⋊4S4 | φ: C3⋊S3/C3 → S3 ⊆ Aut C24 | 36 | 6 | C2^4:2(C3:S3) | 288,917 |
| C24⋊3(C3⋊S3) = C22×C3⋊S4 | φ: C3⋊S3/C3 → S3 ⊆ Aut C24 | 36 | C2^4:3(C3:S3) | 288,1034 | |
| C24⋊4(C3⋊S3) = (C2×C6)⋊S4 | φ: C3⋊S3/C3 → S3 ⊆ Aut C24 | 24 | 6 | C2^4:4(C3:S3) | 288,1036 |
| C24⋊5(C3⋊S3) = C62⋊24D4 | φ: C3⋊S3/C32 → C2 ⊆ Aut C24 | 72 | C2^4:5(C3:S3) | 288,810 | |
| C24⋊6(C3⋊S3) = C22×C32⋊7D4 | φ: C3⋊S3/C32 → C2 ⊆ Aut C24 | 144 | C2^4:6(C3:S3) | 288,1017 |
| extension | φ:Q→Aut N | d | ρ | Label | ID |
|---|---|---|---|---|---|
| C24.(C3⋊S3) = C2×C6.7S4 | φ: C3⋊S3/C3 → S3 ⊆ Aut C24 | 72 | C2^4.(C3:S3) | 288,916 | |
| C24.2(C3⋊S3) = C2×C62⋊5C4 | φ: C3⋊S3/C32 → C2 ⊆ Aut C24 | 144 | C2^4.2(C3:S3) | 288,809 | |
| C24.3(C3⋊S3) = C23×C3⋊Dic3 | central extension (φ=1) | 288 | C2^4.3(C3:S3) | 288,1016 |