# Extensions 1→N→G→Q→1 with N=C14 and Q=C2×M4(2)

Direct product G=N×Q with N=C14 and Q=C2×M4(2)
dρLabelID
M4(2)×C2×C14224M4(2)xC2xC14448,1349

Semidirect products G=N:Q with N=C14 and Q=C2×M4(2)
extensionφ:Q→Aut NdρLabelID
C141(C2×M4(2)) = C22×C8⋊D7φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14224C14:1(C2xM4(2))448,1190
C142(C2×M4(2)) = C2×D7×M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14112C14:2(C2xM4(2))448,1196
C143(C2×M4(2)) = C22×C4.Dic7φ: C2×M4(2)/C22×C4C2 ⊆ Aut C14224C14:3(C2xM4(2))448,1234

Non-split extensions G=N.Q with N=C14 and Q=C2×M4(2)
extensionφ:Q→Aut NdρLabelID
C14.1(C2×M4(2)) = C5611Q8φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14448C14.1(C2xM4(2))448,213
C14.2(C2×M4(2)) = C42.282D14φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14224C14.2(C2xM4(2))448,219
C14.3(C2×M4(2)) = C4×C8⋊D7φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14224C14.3(C2xM4(2))448,221
C14.4(C2×M4(2)) = C86D28φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14224C14.4(C2xM4(2))448,222
C14.5(C2×M4(2)) = D14⋊M4(2)φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14112C14.5(C2xM4(2))448,260
C14.6(C2×M4(2)) = C7⋊C826D4φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14224C14.6(C2xM4(2))448,264
C14.7(C2×M4(2)) = C28.M4(2)φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14448C14.7(C2xM4(2))448,365
C14.8(C2×M4(2)) = C28⋊M4(2)φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14224C14.8(C2xM4(2))448,371
C14.9(C2×M4(2)) = C282M4(2)φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14224C14.9(C2xM4(2))448,372
C14.10(C2×M4(2)) = C2×Dic7⋊C8φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14448C14.10(C2xM4(2))448,633
C14.11(C2×M4(2)) = C2×C56⋊C4φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14448C14.11(C2xM4(2))448,634
C14.12(C2×M4(2)) = C2×D14⋊C8φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14224C14.12(C2xM4(2))448,642
C14.13(C2×M4(2)) = C5632D4φ: C2×M4(2)/C2×C8C2 ⊆ Aut C14224C14.13(C2xM4(2))448,645
C14.14(C2×M4(2)) = C56⋊Q8φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14448C14.14(C2xM4(2))448,235
C14.15(C2×M4(2)) = D7×C8⋊C4φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.15(C2xM4(2))448,238
C14.16(C2×M4(2)) = C42.182D14φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.16(C2xM4(2))448,239
C14.17(C2×M4(2)) = C89D28φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.17(C2xM4(2))448,240
C14.18(C2×M4(2)) = Dic7.C42φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.18(C2xM4(2))448,241
C14.19(C2×M4(2)) = Dic7.5M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.19(C2xM4(2))448,252
C14.20(C2×M4(2)) = Dic7.M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.20(C2xM4(2))448,253
C14.21(C2×M4(2)) = D7×C22⋊C8φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14112C14.21(C2xM4(2))448,258
C14.22(C2×M4(2)) = D142M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.22(C2xM4(2))448,262
C14.23(C2×M4(2)) = Dic7⋊M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.23(C2xM4(2))448,263
C14.24(C2×M4(2)) = C42.27D14φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14448C14.24(C2xM4(2))448,362
C14.25(C2×M4(2)) = D7×C4⋊C8φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.25(C2xM4(2))448,366
C14.26(C2×M4(2)) = C42.200D14φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.26(C2xM4(2))448,367
C14.27(C2×M4(2)) = C42.202D14φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.27(C2xM4(2))448,369
C14.28(C2×M4(2)) = D143M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.28(C2xM4(2))448,370
C14.29(C2×M4(2)) = M4(2)×Dic7φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.29(C2xM4(2))448,651
C14.30(C2×M4(2)) = Dic74M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.30(C2xM4(2))448,652
C14.31(C2×M4(2)) = D146M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14112C14.31(C2xM4(2))448,660
C14.32(C2×M4(2)) = C56⋊D4φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.32(C2xM4(2))448,661
C14.33(C2×M4(2)) = C5618D4φ: C2×M4(2)/M4(2)C2 ⊆ Aut C14224C14.33(C2xM4(2))448,662
C14.34(C2×M4(2)) = C2×C42.D7φ: C2×M4(2)/C22×C4C2 ⊆ Aut C14448C14.34(C2xM4(2))448,455
C14.35(C2×M4(2)) = C4×C4.Dic7φ: C2×M4(2)/C22×C4C2 ⊆ Aut C14224C14.35(C2xM4(2))448,456
C14.36(C2×M4(2)) = C2×C28⋊C8φ: C2×M4(2)/C22×C4C2 ⊆ Aut C14448C14.36(C2xM4(2))448,457
C14.37(C2×M4(2)) = C287M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C14224C14.37(C2xM4(2))448,458
C14.38(C2×M4(2)) = C42.6Dic7φ: C2×M4(2)/C22×C4C2 ⊆ Aut C14224C14.38(C2xM4(2))448,459
C14.39(C2×M4(2)) = C42.7Dic7φ: C2×M4(2)/C22×C4C2 ⊆ Aut C14224C14.39(C2xM4(2))448,460
C14.40(C2×M4(2)) = C42.47D14φ: C2×M4(2)/C22×C4C2 ⊆ Aut C14224C14.40(C2xM4(2))448,545
C14.41(C2×M4(2)) = C283M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C14224C14.41(C2xM4(2))448,546
C14.42(C2×M4(2)) = C42.210D14φ: C2×M4(2)/C22×C4C2 ⊆ Aut C14448C14.42(C2xM4(2))448,558
C14.43(C2×M4(2)) = C2×C28.55D4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C14224C14.43(C2xM4(2))448,740
C14.44(C2×M4(2)) = C24.4Dic7φ: C2×M4(2)/C22×C4C2 ⊆ Aut C14112C14.44(C2xM4(2))448,741
C14.45(C2×M4(2)) = C14×C8⋊C4central extension (φ=1)448C14.45(C2xM4(2))448,811
C14.46(C2×M4(2)) = M4(2)×C28central extension (φ=1)224C14.46(C2xM4(2))448,812
C14.47(C2×M4(2)) = C14×C22⋊C8central extension (φ=1)224C14.47(C2xM4(2))448,814
C14.48(C2×M4(2)) = C7×C24.4C4central extension (φ=1)112C14.48(C2xM4(2))448,815
C14.49(C2×M4(2)) = C14×C4⋊C8central extension (φ=1)448C14.49(C2xM4(2))448,830
C14.50(C2×M4(2)) = C7×C4⋊M4(2)central extension (φ=1)224C14.50(C2xM4(2))448,831
C14.51(C2×M4(2)) = C7×C42.12C4central extension (φ=1)224C14.51(C2xM4(2))448,839
C14.52(C2×M4(2)) = C7×C42.6C4central extension (φ=1)224C14.52(C2xM4(2))448,840
C14.53(C2×M4(2)) = C7×C89D4central extension (φ=1)224C14.53(C2xM4(2))448,843
C14.54(C2×M4(2)) = C7×C86D4central extension (φ=1)224C14.54(C2xM4(2))448,844
C14.55(C2×M4(2)) = C7×C84Q8central extension (φ=1)448C14.55(C2xM4(2))448,854

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