# Extensions 1→N→G→Q→1 with N=C2×C6 and Q=C2×C14

Direct product G=N×Q with N=C2×C6 and Q=C2×C14
dρLabelID
C23×C42336C2^3xC42336,228

Semidirect products G=N:Q with N=C2×C6 and Q=C2×C14
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊(C2×C14) = S3×C7×D4φ: C2×C14/C7C22 ⊆ Aut C2×C6844(C2xC6):(C2xC14)336,188
(C2×C6)⋊2(C2×C14) = D4×C42φ: C2×C14/C14C2 ⊆ Aut C2×C6168(C2xC6):2(C2xC14)336,205
(C2×C6)⋊3(C2×C14) = C14×C3⋊D4φ: C2×C14/C14C2 ⊆ Aut C2×C6168(C2xC6):3(C2xC14)336,193
(C2×C6)⋊4(C2×C14) = S3×C22×C14φ: C2×C14/C14C2 ⊆ Aut C2×C6168(C2xC6):4(C2xC14)336,226

Non-split extensions G=N.Q with N=C2×C6 and Q=C2×C14
extensionφ:Q→Aut NdρLabelID
(C2×C6).(C2×C14) = C7×D42S3φ: C2×C14/C7C22 ⊆ Aut C2×C61684(C2xC6).(C2xC14)336,189
(C2×C6).2(C2×C14) = C4○D4×C21φ: C2×C14/C14C2 ⊆ Aut C2×C61682(C2xC6).2(C2xC14)336,207
(C2×C6).3(C2×C14) = Dic3×C28φ: C2×C14/C14C2 ⊆ Aut C2×C6336(C2xC6).3(C2xC14)336,81
(C2×C6).4(C2×C14) = C7×Dic3⋊C4φ: C2×C14/C14C2 ⊆ Aut C2×C6336(C2xC6).4(C2xC14)336,82
(C2×C6).5(C2×C14) = C7×C4⋊Dic3φ: C2×C14/C14C2 ⊆ Aut C2×C6336(C2xC6).5(C2xC14)336,83
(C2×C6).6(C2×C14) = C7×D6⋊C4φ: C2×C14/C14C2 ⊆ Aut C2×C6168(C2xC6).6(C2xC14)336,84
(C2×C6).7(C2×C14) = C7×C6.D4φ: C2×C14/C14C2 ⊆ Aut C2×C6168(C2xC6).7(C2xC14)336,89
(C2×C6).8(C2×C14) = C14×Dic6φ: C2×C14/C14C2 ⊆ Aut C2×C6336(C2xC6).8(C2xC14)336,184
(C2×C6).9(C2×C14) = S3×C2×C28φ: C2×C14/C14C2 ⊆ Aut C2×C6168(C2xC6).9(C2xC14)336,185
(C2×C6).10(C2×C14) = C14×D12φ: C2×C14/C14C2 ⊆ Aut C2×C6168(C2xC6).10(C2xC14)336,186
(C2×C6).11(C2×C14) = C7×C4○D12φ: C2×C14/C14C2 ⊆ Aut C2×C61682(C2xC6).11(C2xC14)336,187
(C2×C6).12(C2×C14) = Dic3×C2×C14φ: C2×C14/C14C2 ⊆ Aut C2×C6336(C2xC6).12(C2xC14)336,192
(C2×C6).13(C2×C14) = C22⋊C4×C21central extension (φ=1)168(C2xC6).13(C2xC14)336,107
(C2×C6).14(C2×C14) = C4⋊C4×C21central extension (φ=1)336(C2xC6).14(C2xC14)336,108
(C2×C6).15(C2×C14) = Q8×C42central extension (φ=1)336(C2xC6).15(C2xC14)336,206

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