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Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C2×C22

Direct product G=N×Q with N=C2×C4 and Q=C2×C22
dρLabelID
C23×C44352C2^3xC44352,188

Semidirect products G=N:Q with N=C2×C4 and Q=C2×C22
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C2×C22) = C11×C22≀C2φ: C2×C22/C11 → C22 ⊆ Aut C2×C488(C2xC4):1(C2xC22)352,155
(C2×C4)⋊2(C2×C22) = C11×2+ 1+4φ: C2×C22/C11 → C22 ⊆ Aut C2×C4884(C2xC4):2(C2xC22)352,192
(C2×C4)⋊3(C2×C22) = C22⋊C4×C22φ: C2×C22/C22 → C2 ⊆ Aut C2×C4176(C2xC4):3(C2xC22)352,150
(C2×C4)⋊4(C2×C22) = D4×C2×C22φ: C2×C22/C22 → C2 ⊆ Aut C2×C4176(C2xC4):4(C2xC22)352,189
(C2×C4)⋊5(C2×C22) = C4○D4×C22φ: C2×C22/C22 → C2 ⊆ Aut C2×C4176(C2xC4):5(C2xC22)352,191

Non-split extensions G=N.Q with N=C2×C4 and Q=C2×C22
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C2×C22) = C11×C4.D4φ: C2×C22/C11 → C22 ⊆ Aut C2×C4884(C2xC4).1(C2xC22)352,49
(C2×C4).2(C2×C22) = C11×C4.10D4φ: C2×C22/C11 → C22 ⊆ Aut C2×C41764(C2xC4).2(C2xC22)352,50
(C2×C4).3(C2×C22) = C11×C4⋊D4φ: C2×C22/C11 → C22 ⊆ Aut C2×C4176(C2xC4).3(C2xC22)352,156
(C2×C4).4(C2×C22) = C11×C22⋊Q8φ: C2×C22/C11 → C22 ⊆ Aut C2×C4176(C2xC4).4(C2xC22)352,157
(C2×C4).5(C2×C22) = C11×C22.D4φ: C2×C22/C11 → C22 ⊆ Aut C2×C4176(C2xC4).5(C2xC22)352,158
(C2×C4).6(C2×C22) = C11×C4.4D4φ: C2×C22/C11 → C22 ⊆ Aut C2×C4176(C2xC4).6(C2xC22)352,159
(C2×C4).7(C2×C22) = C11×C42.C2φ: C2×C22/C11 → C22 ⊆ Aut C2×C4352(C2xC4).7(C2xC22)352,160
(C2×C4).8(C2×C22) = C11×C42⋊2C2φ: C2×C22/C11 → C22 ⊆ Aut C2×C4176(C2xC4).8(C2xC22)352,161
(C2×C4).9(C2×C22) = C11×C4⋊Q8φ: C2×C22/C11 → C22 ⊆ Aut C2×C4352(C2xC4).9(C2xC22)352,163
(C2×C4).10(C2×C22) = C11×C8⋊C22φ: C2×C22/C11 → C22 ⊆ Aut C2×C4884(C2xC4).10(C2xC22)352,171
(C2×C4).11(C2×C22) = C11×C8.C22φ: C2×C22/C11 → C22 ⊆ Aut C2×C41764(C2xC4).11(C2xC22)352,172
(C2×C4).12(C2×C22) = C11×2- 1+4φ: C2×C22/C11 → C22 ⊆ Aut C2×C41764(C2xC4).12(C2xC22)352,193
(C2×C4).13(C2×C22) = C4⋊C4×C22φ: C2×C22/C22 → C2 ⊆ Aut C2×C4352(C2xC4).13(C2xC22)352,151
(C2×C4).14(C2×C22) = C11×C42⋊C2φ: C2×C22/C22 → C2 ⊆ Aut C2×C4176(C2xC4).14(C2xC22)352,152
(C2×C4).15(C2×C22) = D4×C44φ: C2×C22/C22 → C2 ⊆ Aut C2×C4176(C2xC4).15(C2xC22)352,153
(C2×C4).16(C2×C22) = Q8×C44φ: C2×C22/C22 → C2 ⊆ Aut C2×C4352(C2xC4).16(C2xC22)352,154
(C2×C4).17(C2×C22) = C11×D4⋊C4φ: C2×C22/C22 → C2 ⊆ Aut C2×C4176(C2xC4).17(C2xC22)352,51
(C2×C4).18(C2×C22) = C11×Q8⋊C4φ: C2×C22/C22 → C2 ⊆ Aut C2×C4352(C2xC4).18(C2xC22)352,52
(C2×C4).19(C2×C22) = C11×C4≀C2φ: C2×C22/C22 → C2 ⊆ Aut C2×C4882(C2xC4).19(C2xC22)352,53
(C2×C4).20(C2×C22) = C11×C4.Q8φ: C2×C22/C22 → C2 ⊆ Aut C2×C4352(C2xC4).20(C2xC22)352,55
(C2×C4).21(C2×C22) = C11×C2.D8φ: C2×C22/C22 → C2 ⊆ Aut C2×C4352(C2xC4).21(C2xC22)352,56
(C2×C4).22(C2×C22) = C11×C8.C4φ: C2×C22/C22 → C2 ⊆ Aut C2×C41762(C2xC4).22(C2xC22)352,57
(C2×C4).23(C2×C22) = C11×C4⋊1D4φ: C2×C22/C22 → C2 ⊆ Aut C2×C4176(C2xC4).23(C2xC22)352,162
(C2×C4).24(C2×C22) = C11×C8○D4φ: C2×C22/C22 → C2 ⊆ Aut C2×C41762(C2xC4).24(C2xC22)352,166
(C2×C4).25(C2×C22) = D8×C22φ: C2×C22/C22 → C2 ⊆ Aut C2×C4176(C2xC4).25(C2xC22)352,167
(C2×C4).26(C2×C22) = SD16×C22φ: C2×C22/C22 → C2 ⊆ Aut C2×C4176(C2xC4).26(C2xC22)352,168
(C2×C4).27(C2×C22) = Q16×C22φ: C2×C22/C22 → C2 ⊆ Aut C2×C4352(C2xC4).27(C2xC22)352,169
(C2×C4).28(C2×C22) = C11×C4○D8φ: C2×C22/C22 → C2 ⊆ Aut C2×C41762(C2xC4).28(C2xC22)352,170
(C2×C4).29(C2×C22) = Q8×C2×C22φ: C2×C22/C22 → C2 ⊆ Aut C2×C4352(C2xC4).29(C2xC22)352,190
(C2×C4).30(C2×C22) = C11×C8⋊C4central extension (φ=1)352(C2xC4).30(C2xC22)352,46
(C2×C4).31(C2×C22) = C11×C22⋊C8central extension (φ=1)176(C2xC4).31(C2xC22)352,47
(C2×C4).32(C2×C22) = C11×C4⋊C8central extension (φ=1)352(C2xC4).32(C2xC22)352,54
(C2×C4).33(C2×C22) = M4(2)×C22central extension (φ=1)176(C2xC4).33(C2xC22)352,165

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