Extensions 1→N→G→Q→1 with N=D20 and Q=S3

Direct product G=NxQ with N=D20 and Q=S3
dρLabelID
S3xD20604+S3xD20240,137

Semidirect products G=N:Q with N=D20 and Q=S3
extensionφ:Q→Out NdρLabelID
D20:1S3 = C3:D40φ: S3/C3C2 ⊆ Out D201204+D20:1S3240,14
D20:2S3 = C15:D8φ: S3/C3C2 ⊆ Out D201204D20:2S3240,13
D20:3S3 = D20:S3φ: S3/C3C2 ⊆ Out D201204D20:3S3240,127
D20:4S3 = C20:D6φ: S3/C3C2 ⊆ Out D20604D20:4S3240,138
D20:5S3 = D20:5S3φ: trivial image1204-D20:5S3240,126

Non-split extensions G=N.Q with N=D20 and Q=S3
extensionφ:Q→Out NdρLabelID
D20.1S3 = C6.D20φ: S3/C3C2 ⊆ Out D201204-D20.1S3240,18
D20.2S3 = C30.D4φ: S3/C3C2 ⊆ Out D201204D20.2S3240,16

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