# Extensions 1→N→G→Q→1 with N=C2×C4 and Q=Q8

Direct product G=N×Q with N=C2×C4 and Q=Q8
dρLabelID
C2×C4×Q864C2xC4xQ864,197

Semidirect products G=N:Q with N=C2×C4 and Q=Q8
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1Q8 = C23.78C23φ: Q8/C2C22 ⊆ Aut C2×C464(C2xC4):1Q864,76
(C2×C4)⋊2Q8 = C23.41C23φ: Q8/C2C22 ⊆ Aut C2×C432(C2xC4):2Q864,225
(C2×C4)⋊3Q8 = C23.67C23φ: Q8/C4C2 ⊆ Aut C2×C464(C2xC4):3Q864,72
(C2×C4)⋊4Q8 = C2×C4⋊Q8φ: Q8/C4C2 ⊆ Aut C2×C464(C2xC4):4Q864,212
(C2×C4)⋊5Q8 = C23.37C23φ: Q8/C4C2 ⊆ Aut C2×C432(C2xC4):5Q864,214

Non-split extensions G=N.Q with N=C2×C4 and Q=Q8
extensionφ:Q→Aut NdρLabelID
(C2×C4).1Q8 = C4.9C42φ: Q8/C2C22 ⊆ Aut C2×C4164(C2xC4).1Q864,18
(C2×C4).2Q8 = C22.C42φ: Q8/C2C22 ⊆ Aut C2×C432(C2xC4).2Q864,24
(C2×C4).3Q8 = M4(2)⋊4C4φ: Q8/C2C22 ⊆ Aut C2×C4164(C2xC4).3Q864,25
(C2×C4).4Q8 = C23.81C23φ: Q8/C2C22 ⊆ Aut C2×C464(C2xC4).4Q864,79
(C2×C4).5Q8 = C23.83C23φ: Q8/C2C22 ⊆ Aut C2×C464(C2xC4).5Q864,81
(C2×C4).6Q8 = M4(2)⋊C4φ: Q8/C2C22 ⊆ Aut C2×C432(C2xC4).6Q864,109
(C2×C4).7Q8 = M4(2).C4φ: Q8/C2C22 ⊆ Aut C2×C4164(C2xC4).7Q864,111
(C2×C4).8Q8 = C82C8φ: Q8/C4C2 ⊆ Aut C2×C464(C2xC4).8Q864,15
(C2×C4).9Q8 = C81C8φ: Q8/C4C2 ⊆ Aut C2×C464(C2xC4).9Q864,16
(C2×C4).10Q8 = C23.63C23φ: Q8/C4C2 ⊆ Aut C2×C464(C2xC4).10Q864,68
(C2×C4).11Q8 = C426C4φ: Q8/C4C2 ⊆ Aut C2×C416(C2xC4).11Q864,20
(C2×C4).12Q8 = C22.4Q16φ: Q8/C4C2 ⊆ Aut C2×C464(C2xC4).12Q864,21
(C2×C4).13Q8 = C428C4φ: Q8/C4C2 ⊆ Aut C2×C464(C2xC4).13Q864,63
(C2×C4).14Q8 = C429C4φ: Q8/C4C2 ⊆ Aut C2×C464(C2xC4).14Q864,65
(C2×C4).15Q8 = C23.65C23φ: Q8/C4C2 ⊆ Aut C2×C464(C2xC4).15Q864,70
(C2×C4).16Q8 = C4⋊M4(2)φ: Q8/C4C2 ⊆ Aut C2×C432(C2xC4).16Q864,104
(C2×C4).17Q8 = C42.6C22φ: Q8/C4C2 ⊆ Aut C2×C432(C2xC4).17Q864,105
(C2×C4).18Q8 = C2×C4.Q8φ: Q8/C4C2 ⊆ Aut C2×C464(C2xC4).18Q864,106
(C2×C4).19Q8 = C2×C2.D8φ: Q8/C4C2 ⊆ Aut C2×C464(C2xC4).19Q864,107
(C2×C4).20Q8 = C23.25D4φ: Q8/C4C2 ⊆ Aut C2×C432(C2xC4).20Q864,108
(C2×C4).21Q8 = C2×C8.C4φ: Q8/C4C2 ⊆ Aut C2×C432(C2xC4).21Q864,110
(C2×C4).22Q8 = C2×C42.C2φ: Q8/C4C2 ⊆ Aut C2×C464(C2xC4).22Q864,208
(C2×C4).23Q8 = C22.7C42central extension (φ=1)64(C2xC4).23Q864,17
(C2×C4).24Q8 = C4×C4⋊C4central extension (φ=1)64(C2xC4).24Q864,59
(C2×C4).25Q8 = C2×C4⋊C8central extension (φ=1)64(C2xC4).25Q864,103

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