# Extensions 1→N→G→Q→1 with N=C33 and Q=S3

Direct product G=N×Q with N=C33 and Q=S3
dρLabelID
S3×C3354S3xC3^3162,51

Semidirect products G=N:Q with N=C33 and Q=S3
extensionφ:Q→Aut NdρLabelID
C331S3 = C3≀S3φ: S3/C1S3 ⊆ Aut C3393C3^3:1S3162,10
C332S3 = C33⋊S3φ: S3/C1S3 ⊆ Aut C3396+C3^3:2S3162,19
C333S3 = C3×C32⋊C6φ: S3/C1S3 ⊆ Aut C33186C3^3:3S3162,34
C334S3 = He34S3φ: S3/C1S3 ⊆ Aut C3327C3^3:4S3162,40
C335S3 = C3×He3⋊C2φ: S3/C1S3 ⊆ Aut C3327C3^3:5S3162,41
C336S3 = He35S3φ: S3/C1S3 ⊆ Aut C33186C3^3:6S3162,46
C337S3 = C32×C3⋊S3φ: S3/C3C2 ⊆ Aut C3318C3^3:7S3162,52
C338S3 = C3×C33⋊C2φ: S3/C3C2 ⊆ Aut C3354C3^3:8S3162,53
C339S3 = C34⋊C2φ: S3/C3C2 ⊆ Aut C3381C3^3:9S3162,54

Non-split extensions G=N.Q with N=C33 and Q=S3
extensionφ:Q→Aut NdρLabelID
C33.1S3 = C32⋊D9φ: S3/C1S3 ⊆ Aut C3327C3^3.1S3162,5
C33.2S3 = C322D9φ: S3/C1S3 ⊆ Aut C33186C3^3.2S3162,17
C33.3S3 = C3×C9⋊C6φ: S3/C1S3 ⊆ Aut C33186C3^3.3S3162,36
C33.4S3 = C33.S3φ: S3/C1S3 ⊆ Aut C3327C3^3.4S3162,42
C33.5S3 = C32×D9φ: S3/C3C2 ⊆ Aut C3354C3^3.5S3162,32
C33.6S3 = C3×C9⋊S3φ: S3/C3C2 ⊆ Aut C3354C3^3.6S3162,38
C33.7S3 = C324D9φ: S3/C3C2 ⊆ Aut C3381C3^3.7S3162,45

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