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Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C2×C14

Direct product G=N×Q with N=C2×C4 and Q=C2×C14
dρLabelID
C23×C28224C2^3xC28224,189

Semidirect products G=N:Q with N=C2×C4 and Q=C2×C14
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C2×C14) = C7×C22≀C2φ: C2×C14/C7 → C22 ⊆ Aut C2×C456(C2xC4):1(C2xC14)224,155
(C2×C4)⋊2(C2×C14) = C7×2+ 1+4φ: C2×C14/C7 → C22 ⊆ Aut C2×C4564(C2xC4):2(C2xC14)224,193
(C2×C4)⋊3(C2×C14) = C14×C22⋊C4φ: C2×C14/C14 → C2 ⊆ Aut C2×C4112(C2xC4):3(C2xC14)224,150
(C2×C4)⋊4(C2×C14) = D4×C2×C14φ: C2×C14/C14 → C2 ⊆ Aut C2×C4112(C2xC4):4(C2xC14)224,190
(C2×C4)⋊5(C2×C14) = C14×C4○D4φ: C2×C14/C14 → C2 ⊆ Aut C2×C4112(C2xC4):5(C2xC14)224,192

Non-split extensions G=N.Q with N=C2×C4 and Q=C2×C14
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C2×C14) = C7×C4.D4φ: C2×C14/C7 → C22 ⊆ Aut C2×C4564(C2xC4).1(C2xC14)224,49
(C2×C4).2(C2×C14) = C7×C4.10D4φ: C2×C14/C7 → C22 ⊆ Aut C2×C41124(C2xC4).2(C2xC14)224,50
(C2×C4).3(C2×C14) = C7×C4⋊D4φ: C2×C14/C7 → C22 ⊆ Aut C2×C4112(C2xC4).3(C2xC14)224,156
(C2×C4).4(C2×C14) = C7×C22⋊Q8φ: C2×C14/C7 → C22 ⊆ Aut C2×C4112(C2xC4).4(C2xC14)224,157
(C2×C4).5(C2×C14) = C7×C22.D4φ: C2×C14/C7 → C22 ⊆ Aut C2×C4112(C2xC4).5(C2xC14)224,158
(C2×C4).6(C2×C14) = C7×C4.4D4φ: C2×C14/C7 → C22 ⊆ Aut C2×C4112(C2xC4).6(C2xC14)224,159
(C2×C4).7(C2×C14) = C7×C42.C2φ: C2×C14/C7 → C22 ⊆ Aut C2×C4224(C2xC4).7(C2xC14)224,160
(C2×C4).8(C2×C14) = C7×C42⋊2C2φ: C2×C14/C7 → C22 ⊆ Aut C2×C4112(C2xC4).8(C2xC14)224,161
(C2×C4).9(C2×C14) = C7×C4⋊Q8φ: C2×C14/C7 → C22 ⊆ Aut C2×C4224(C2xC4).9(C2xC14)224,163
(C2×C4).10(C2×C14) = C7×C8⋊C22φ: C2×C14/C7 → C22 ⊆ Aut C2×C4564(C2xC4).10(C2xC14)224,171
(C2×C4).11(C2×C14) = C7×C8.C22φ: C2×C14/C7 → C22 ⊆ Aut C2×C41124(C2xC4).11(C2xC14)224,172
(C2×C4).12(C2×C14) = C7×2- 1+4φ: C2×C14/C7 → C22 ⊆ Aut C2×C41124(C2xC4).12(C2xC14)224,194
(C2×C4).13(C2×C14) = C14×C4⋊C4φ: C2×C14/C14 → C2 ⊆ Aut C2×C4224(C2xC4).13(C2xC14)224,151
(C2×C4).14(C2×C14) = C7×C42⋊C2φ: C2×C14/C14 → C2 ⊆ Aut C2×C4112(C2xC4).14(C2xC14)224,152
(C2×C4).15(C2×C14) = D4×C28φ: C2×C14/C14 → C2 ⊆ Aut C2×C4112(C2xC4).15(C2xC14)224,153
(C2×C4).16(C2×C14) = Q8×C28φ: C2×C14/C14 → C2 ⊆ Aut C2×C4224(C2xC4).16(C2xC14)224,154
(C2×C4).17(C2×C14) = C7×D4⋊C4φ: C2×C14/C14 → C2 ⊆ Aut C2×C4112(C2xC4).17(C2xC14)224,51
(C2×C4).18(C2×C14) = C7×Q8⋊C4φ: C2×C14/C14 → C2 ⊆ Aut C2×C4224(C2xC4).18(C2xC14)224,52
(C2×C4).19(C2×C14) = C7×C4≀C2φ: C2×C14/C14 → C2 ⊆ Aut C2×C4562(C2xC4).19(C2xC14)224,53
(C2×C4).20(C2×C14) = C7×C4.Q8φ: C2×C14/C14 → C2 ⊆ Aut C2×C4224(C2xC4).20(C2xC14)224,55
(C2×C4).21(C2×C14) = C7×C2.D8φ: C2×C14/C14 → C2 ⊆ Aut C2×C4224(C2xC4).21(C2xC14)224,56
(C2×C4).22(C2×C14) = C7×C8.C4φ: C2×C14/C14 → C2 ⊆ Aut C2×C41122(C2xC4).22(C2xC14)224,57
(C2×C4).23(C2×C14) = C7×C4⋊1D4φ: C2×C14/C14 → C2 ⊆ Aut C2×C4112(C2xC4).23(C2xC14)224,162
(C2×C4).24(C2×C14) = C7×C8○D4φ: C2×C14/C14 → C2 ⊆ Aut C2×C41122(C2xC4).24(C2xC14)224,166
(C2×C4).25(C2×C14) = C14×D8φ: C2×C14/C14 → C2 ⊆ Aut C2×C4112(C2xC4).25(C2xC14)224,167
(C2×C4).26(C2×C14) = C14×SD16φ: C2×C14/C14 → C2 ⊆ Aut C2×C4112(C2xC4).26(C2xC14)224,168
(C2×C4).27(C2×C14) = C14×Q16φ: C2×C14/C14 → C2 ⊆ Aut C2×C4224(C2xC4).27(C2xC14)224,169
(C2×C4).28(C2×C14) = C7×C4○D8φ: C2×C14/C14 → C2 ⊆ Aut C2×C41122(C2xC4).28(C2xC14)224,170
(C2×C4).29(C2×C14) = Q8×C2×C14φ: C2×C14/C14 → C2 ⊆ Aut C2×C4224(C2xC4).29(C2xC14)224,191
(C2×C4).30(C2×C14) = C7×C8⋊C4central extension (φ=1)224(C2xC4).30(C2xC14)224,46
(C2×C4).31(C2×C14) = C7×C22⋊C8central extension (φ=1)112(C2xC4).31(C2xC14)224,47
(C2×C4).32(C2×C14) = C7×C4⋊C8central extension (φ=1)224(C2xC4).32(C2xC14)224,54
(C2×C4).33(C2×C14) = C14×M4(2)central extension (φ=1)112(C2xC4).33(C2xC14)224,165

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