# Extensions 1→N→G→Q→1 with N=C62 and Q=S3

Direct product G=N×Q with N=C62 and Q=S3
dρLabelID
S3×C6272S3xC6^2216,174

Semidirect products G=N:Q with N=C62 and Q=S3
extensionφ:Q→Aut NdρLabelID
C621S3 = C32×S4φ: S3/C1S3 ⊆ Aut C6236C6^2:1S3216,163
C622S3 = He36D4φ: S3/C1S3 ⊆ Aut C62366C6^2:2S3216,60
C623S3 = He37D4φ: S3/C1S3 ⊆ Aut C62366C6^2:3S3216,72
C624S3 = C62⋊S3φ: S3/C1S3 ⊆ Aut C62186+C6^2:4S3216,92
C625S3 = C32⋊S4φ: S3/C1S3 ⊆ Aut C62183C6^2:5S3216,95
C626S3 = C22×C32⋊C6φ: S3/C1S3 ⊆ Aut C6236C6^2:6S3216,110
C627S3 = C22×He3⋊C2φ: S3/C1S3 ⊆ Aut C6236C6^2:7S3216,113
C628S3 = C3×C3⋊S4φ: S3/C1S3 ⊆ Aut C62246C6^2:8S3216,164
C629S3 = C324S4φ: S3/C1S3 ⊆ Aut C6236C6^2:9S3216,165
C6210S3 = C32×C3⋊D4φ: S3/C3C2 ⊆ Aut C6236C6^2:10S3216,139
C6211S3 = C3×C327D4φ: S3/C3C2 ⊆ Aut C6236C6^2:11S3216,144
C6212S3 = C3315D4φ: S3/C3C2 ⊆ Aut C62108C6^2:12S3216,149
C6213S3 = C2×C6×C3⋊S3φ: S3/C3C2 ⊆ Aut C6272C6^2:13S3216,175
C6214S3 = C22×C33⋊C2φ: S3/C3C2 ⊆ Aut C62108C6^2:14S3216,176

Non-split extensions G=N.Q with N=C62 and Q=S3
extensionφ:Q→Aut NdρLabelID
C62.1S3 = C2×C32⋊C12φ: S3/C1S3 ⊆ Aut C6272C6^2.1S3216,59
C62.2S3 = C2×C9⋊C12φ: S3/C1S3 ⊆ Aut C6272C6^2.2S3216,61
C62.3S3 = Dic9⋊C6φ: S3/C1S3 ⊆ Aut C62366C6^2.3S3216,62
C62.4S3 = C2×He33C4φ: S3/C1S3 ⊆ Aut C6272C6^2.4S3216,71
C62.5S3 = C32.S4φ: S3/C1S3 ⊆ Aut C62186+C6^2.5S3216,90
C62.6S3 = C3×C3.S4φ: S3/C1S3 ⊆ Aut C62366C6^2.6S3216,91
C62.7S3 = C32.3S4φ: S3/C1S3 ⊆ Aut C6254C6^2.7S3216,94
C62.8S3 = C22×C9⋊C6φ: S3/C1S3 ⊆ Aut C6236C6^2.8S3216,111
C62.9S3 = C6×Dic9φ: S3/C3C2 ⊆ Aut C6272C6^2.9S3216,55
C62.10S3 = C3×C9⋊D4φ: S3/C3C2 ⊆ Aut C62362C6^2.10S3216,57
C62.11S3 = C2×C9⋊Dic3φ: S3/C3C2 ⊆ Aut C62216C6^2.11S3216,69
C62.12S3 = C6.D18φ: S3/C3C2 ⊆ Aut C62108C6^2.12S3216,70
C62.13S3 = C2×C6×D9φ: S3/C3C2 ⊆ Aut C6272C6^2.13S3216,108
C62.14S3 = C22×C9⋊S3φ: S3/C3C2 ⊆ Aut C62108C6^2.14S3216,112
C62.15S3 = C6×C3⋊Dic3φ: S3/C3C2 ⊆ Aut C6272C6^2.15S3216,143
C62.16S3 = C2×C335C4φ: S3/C3C2 ⊆ Aut C62216C6^2.16S3216,148
C62.17S3 = Dic3×C3×C6central extension (φ=1)72C6^2.17S3216,138

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