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Extensions 1→N→G→Q→1 with N=C3:Dic3 and Q=S3

Direct product G=NxQ with N=C3:Dic3 and Q=S3
dρLabelID
S3xC3:Dic372S3xC3:Dic3216,124

Semidirect products G=N:Q with N=C3:Dic3 and Q=S3
extensionφ:Q→Out NdρLabelID
C3:Dic3:1S3 = C6.S32φ: S3/C1 → S3 ⊆ Out C3:Dic3366C3:Dic3:1S3216,34
C3:Dic3:2S3 = He3:(C2xC4)φ: S3/C1 → S3 ⊆ Out C3:Dic3366-C3:Dic3:2S3216,36
C3:Dic3:3S3 = He3:3D4φ: S3/C1 → S3 ⊆ Out C3:Dic3366C3:Dic3:3S3216,37
C3:Dic3:4S3 = C33:7D4φ: S3/C3 → C2 ⊆ Out C3:Dic336C3:Dic3:4S3216,128
C3:Dic3:5S3 = C33:9(C2xC4)φ: S3/C3 → C2 ⊆ Out C3:Dic3244C3:Dic3:5S3216,131
C3:Dic3:6S3 = C33:9D4φ: S3/C3 → C2 ⊆ Out C3:Dic3244C3:Dic3:6S3216,132
C3:Dic3:7S3 = C33:8(C2xC4)φ: trivial image36C3:Dic3:7S3216,126

Non-split extensions G=N.Q with N=C3:Dic3 and Q=S3
extensionφ:Q→Out NdρLabelID
C3:Dic3.S3 = He3:2Q8φ: S3/C1 → S3 ⊆ Out C3:Dic3726-C3:Dic3.S3216,33
C3:Dic3.2S3 = C33:4C8φ: S3/C3 → C2 ⊆ Out C3:Dic3244C3:Dic3.2S3216,118
C3:Dic3.3S3 = C33:4Q8φ: S3/C3 → C2 ⊆ Out C3:Dic372C3:Dic3.3S3216,130
C3:Dic3.4S3 = C33:5Q8φ: S3/C3 → C2 ⊆ Out C3:Dic3244C3:Dic3.4S3216,133

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