Extensions 1→N→G→Q→1 with N=C6 and Q=C3×C4⋊C4

Direct product G=N×Q with N=C6 and Q=C3×C4⋊C4
dρLabelID
C4⋊C4×C3×C6288C4:C4xC3xC6288,813

Semidirect products G=N:Q with N=C6 and Q=C3×C4⋊C4
extensionφ:Q→Aut NdρLabelID
C61(C3×C4⋊C4) = C6×Dic3⋊C4φ: C3×C4⋊C4/C2×C12C2 ⊆ Aut C696C6:1(C3xC4:C4)288,694
C62(C3×C4⋊C4) = C6×C4⋊Dic3φ: C3×C4⋊C4/C2×C12C2 ⊆ Aut C696C6:2(C3xC4:C4)288,696

Non-split extensions G=N.Q with N=C6 and Q=C3×C4⋊C4
extensionφ:Q→Aut NdρLabelID
C6.1(C3×C4⋊C4) = C3×C12⋊C8φ: C3×C4⋊C4/C2×C12C2 ⊆ Aut C696C6.1(C3xC4:C4)288,238
C6.2(C3×C4⋊C4) = C3×C6.Q16φ: C3×C4⋊C4/C2×C12C2 ⊆ Aut C696C6.2(C3xC4:C4)288,241
C6.3(C3×C4⋊C4) = C3×C12.Q8φ: C3×C4⋊C4/C2×C12C2 ⊆ Aut C696C6.3(C3xC4:C4)288,242
C6.4(C3×C4⋊C4) = C3×Dic3⋊C8φ: C3×C4⋊C4/C2×C12C2 ⊆ Aut C696C6.4(C3xC4:C4)288,248
C6.5(C3×C4⋊C4) = C3×C8⋊Dic3φ: C3×C4⋊C4/C2×C12C2 ⊆ Aut C696C6.5(C3xC4:C4)288,251
C6.6(C3×C4⋊C4) = C3×C241C4φ: C3×C4⋊C4/C2×C12C2 ⊆ Aut C696C6.6(C3xC4:C4)288,252
C6.7(C3×C4⋊C4) = C3×C24.C4φ: C3×C4⋊C4/C2×C12C2 ⊆ Aut C6482C6.7(C3xC4:C4)288,253
C6.8(C3×C4⋊C4) = C3×C12.53D4φ: C3×C4⋊C4/C2×C12C2 ⊆ Aut C6484C6.8(C3xC4:C4)288,256
C6.9(C3×C4⋊C4) = C3×C6.C42φ: C3×C4⋊C4/C2×C12C2 ⊆ Aut C696C6.9(C3xC4:C4)288,265
C6.10(C3×C4⋊C4) = C9×C2.C42central extension (φ=1)288C6.10(C3xC4:C4)288,45
C6.11(C3×C4⋊C4) = C9×C4⋊C8central extension (φ=1)288C6.11(C3xC4:C4)288,55
C6.12(C3×C4⋊C4) = C9×C4.Q8central extension (φ=1)288C6.12(C3xC4:C4)288,56
C6.13(C3×C4⋊C4) = C9×C2.D8central extension (φ=1)288C6.13(C3xC4:C4)288,57
C6.14(C3×C4⋊C4) = C9×C8.C4central extension (φ=1)1442C6.14(C3xC4:C4)288,58
C6.15(C3×C4⋊C4) = C4⋊C4×C18central extension (φ=1)288C6.15(C3xC4:C4)288,166
C6.16(C3×C4⋊C4) = C32×C2.C42central extension (φ=1)288C6.16(C3xC4:C4)288,313
C6.17(C3×C4⋊C4) = C32×C4⋊C8central extension (φ=1)288C6.17(C3xC4:C4)288,323
C6.18(C3×C4⋊C4) = C32×C4.Q8central extension (φ=1)288C6.18(C3xC4:C4)288,324
C6.19(C3×C4⋊C4) = C32×C2.D8central extension (φ=1)288C6.19(C3xC4:C4)288,325
C6.20(C3×C4⋊C4) = C32×C8.C4central extension (φ=1)144C6.20(C3xC4:C4)288,326

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