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Extensions 1→N→G→Q→1 with N=C7×Q8 and Q=C6

Direct product G=N×Q with N=C7×Q8 and Q=C6
dρLabelID
Q8×C42336Q8xC42336,206

Semidirect products G=N:Q with N=C7×Q8 and Q=C6
extensionφ:Q→Out NdρLabelID
(C7×Q8)⋊1C6 = D7×SL2(𝔽3)φ: C6/C1 → C6 ⊆ Out C7×Q8564-(C7xQ8):1C6336,132
(C7×Q8)⋊2C6 = Q8⋊F7φ: C6/C1 → C6 ⊆ Out C7×Q85612-(C7xQ8):2C6336,135
(C7×Q8)⋊3C6 = Q8⋊2F7φ: C6/C1 → C6 ⊆ Out C7×Q85612+(C7xQ8):3C6336,20
(C7×Q8)⋊4C6 = Q8×F7φ: C6/C1 → C6 ⊆ Out C7×Q85612-(C7xQ8):4C6336,127
(C7×Q8)⋊5C6 = Q8⋊3F7φ: C6/C1 → C6 ⊆ Out C7×Q85612+(C7xQ8):5C6336,128
(C7×Q8)⋊6C6 = SD16×C7⋊C3φ: C6/C1 → C6 ⊆ Out C7×Q8566(C7xQ8):6C6336,54
(C7×Q8)⋊7C6 = C14×SL2(𝔽3)φ: C6/C2 → C3 ⊆ Out C7×Q8112(C7xQ8):7C6336,169
(C7×Q8)⋊8C6 = C2×C14.A4φ: C6/C2 → C3 ⊆ Out C7×Q8112(C7xQ8):8C6336,172
(C7×Q8)⋊9C6 = C2×Q8×C7⋊C3φ: C6/C2 → C3 ⊆ Out C7×Q8112(C7xQ8):9C6336,166
(C7×Q8)⋊10C6 = C4○D4×C7⋊C3φ: C6/C2 → C3 ⊆ Out C7×Q8566(C7xQ8):10C6336,167
(C7×Q8)⋊11C6 = C3×Q8⋊D7φ: C6/C3 → C2 ⊆ Out C7×Q81684(C7xQ8):11C6336,71
(C7×Q8)⋊12C6 = C3×Q8×D7φ: C6/C3 → C2 ⊆ Out C7×Q81684(C7xQ8):12C6336,180
(C7×Q8)⋊13C6 = C3×Q8⋊2D7φ: C6/C3 → C2 ⊆ Out C7×Q81684(C7xQ8):13C6336,181
(C7×Q8)⋊14C6 = SD16×C21φ: C6/C3 → C2 ⊆ Out C7×Q81682(C7xQ8):14C6336,112
(C7×Q8)⋊15C6 = C4○D4×C21φ: trivial image1682(C7xQ8):15C6336,207

Non-split extensions G=N.Q with N=C7×Q8 and Q=C6
extensionφ:Q→Out NdρLabelID
(C7×Q8).1C6 = Dic7.2A4φ: C6/C1 → C6 ⊆ Out C7×Q81124+(C7xQ8).1C6336,131
(C7×Q8).2C6 = Q8.F7φ: C6/C1 → C6 ⊆ Out C7×Q811212+(C7xQ8).2C6336,134
(C7×Q8).3C6 = Q8.2F7φ: C6/C1 → C6 ⊆ Out C7×Q811212-(C7xQ8).3C6336,21
(C7×Q8).4C6 = Q16×C7⋊C3φ: C6/C1 → C6 ⊆ Out C7×Q81126(C7xQ8).4C6336,55
(C7×Q8).5C6 = C7×C4.A4φ: C6/C2 → C3 ⊆ Out C7×Q81122(C7xQ8).5C6336,170
(C7×Q8).6C6 = C28.A4φ: C6/C2 → C3 ⊆ Out C7×Q81126(C7xQ8).6C6336,173
(C7×Q8).7C6 = C3×C7⋊Q16φ: C6/C3 → C2 ⊆ Out C7×Q83364(C7xQ8).7C6336,72
(C7×Q8).8C6 = Q16×C21φ: C6/C3 → C2 ⊆ Out C7×Q83362(C7xQ8).8C6336,113

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