# Extensions 1→N→G→Q→1 with N=C6 and Q=S32

Direct product G=N×Q with N=C6 and Q=S32
dρLabelID
S32×C6244S3^2xC6216,170

Semidirect products G=N:Q with N=C6 and Q=S32
extensionφ:Q→Aut NdρLabelID
C61S32 = C2×S3×C3⋊S3φ: S32/C3×S3C2 ⊆ Aut C636C6:1S3^2216,171
C62S32 = C2×C324D6φ: S32/C3⋊S3C2 ⊆ Aut C6244C6:2S3^2216,172

Non-split extensions G=N.Q with N=C6 and Q=S32
extensionφ:Q→Aut NdρLabelID
C6.1S32 = C9⋊Dic6φ: S32/C3×S3C2 ⊆ Aut C6724-C6.1S3^2216,26
C6.2S32 = Dic3×D9φ: S32/C3×S3C2 ⊆ Aut C6724-C6.2S3^2216,27
C6.3S32 = C18.D6φ: S32/C3×S3C2 ⊆ Aut C6364+C6.3S3^2216,28
C6.4S32 = C3⋊D36φ: S32/C3×S3C2 ⊆ Aut C6364+C6.4S3^2216,29
C6.5S32 = S3×Dic9φ: S32/C3×S3C2 ⊆ Aut C6724-C6.5S3^2216,30
C6.6S32 = D6⋊D9φ: S32/C3×S3C2 ⊆ Aut C6724-C6.6S3^2216,31
C6.7S32 = C9⋊D12φ: S32/C3×S3C2 ⊆ Aut C6364+C6.7S3^2216,32
C6.8S32 = C2×S3×D9φ: S32/C3×S3C2 ⊆ Aut C6364+C6.8S3^2216,101
C6.9S32 = S3×C3⋊Dic3φ: S32/C3×S3C2 ⊆ Aut C672C6.9S3^2216,124
C6.10S32 = Dic3×C3⋊S3φ: S32/C3×S3C2 ⊆ Aut C672C6.10S3^2216,125
C6.11S32 = C338(C2×C4)φ: S32/C3×S3C2 ⊆ Aut C636C6.11S3^2216,126
C6.12S32 = C336D4φ: S32/C3×S3C2 ⊆ Aut C672C6.12S3^2216,127
C6.13S32 = C337D4φ: S32/C3×S3C2 ⊆ Aut C636C6.13S3^2216,128
C6.14S32 = C338D4φ: S32/C3×S3C2 ⊆ Aut C636C6.14S3^2216,129
C6.15S32 = C334Q8φ: S32/C3×S3C2 ⊆ Aut C672C6.15S3^2216,130
C6.16S32 = He32Q8φ: S32/C3⋊S3C2 ⊆ Aut C6726-C6.16S3^2216,33
C6.17S32 = C6.S32φ: S32/C3⋊S3C2 ⊆ Aut C6366C6.17S3^2216,34
C6.18S32 = He32D4φ: S32/C3⋊S3C2 ⊆ Aut C6366+C6.18S3^2216,35
C6.19S32 = He3⋊(C2×C4)φ: S32/C3⋊S3C2 ⊆ Aut C6366-C6.19S3^2216,36
C6.20S32 = He33D4φ: S32/C3⋊S3C2 ⊆ Aut C6366C6.20S3^2216,37
C6.21S32 = C2×C32⋊D6φ: S32/C3⋊S3C2 ⊆ Aut C6186+C6.21S3^2216,102
C6.22S32 = C339(C2×C4)φ: S32/C3⋊S3C2 ⊆ Aut C6244C6.22S3^2216,131
C6.23S32 = C339D4φ: S32/C3⋊S3C2 ⊆ Aut C6244C6.23S3^2216,132
C6.24S32 = C335Q8φ: S32/C3⋊S3C2 ⊆ Aut C6244C6.24S3^2216,133
C6.25S32 = C3×S3×Dic3central extension (φ=1)244C6.25S3^2216,119
C6.26S32 = C3×C6.D6central extension (φ=1)244C6.26S3^2216,120
C6.27S32 = C3×D6⋊S3central extension (φ=1)244C6.27S3^2216,121
C6.28S32 = C3×C3⋊D12central extension (φ=1)244C6.28S3^2216,122
C6.29S32 = C3×C322Q8central extension (φ=1)244C6.29S3^2216,123

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