# Extensions 1→N→G→Q→1 with N=C3×C27 and Q=C6

Direct product G=N×Q with N=C3×C27 and Q=C6
dρLabelID
C32×C54486C3^2xC54486,207

Semidirect products G=N:Q with N=C3×C27 and Q=C6
extensionφ:Q→Aut NdρLabelID
(C3×C27)⋊1C6 = C32⋊D27φ: C6/C1C6 ⊆ Aut C3×C2781(C3xC27):1C6486,17
(C3×C27)⋊2C6 = He3.D9φ: C6/C1C6 ⊆ Aut C3×C27816+(C3xC27):2C6486,27
(C3×C27)⋊3C6 = He3.2D9φ: C6/C1C6 ⊆ Aut C3×C27816+(C3xC27):3C6486,29
(C3×C27)⋊4C6 = C3×C27⋊C6φ: C6/C1C6 ⊆ Aut C3×C27546(C3xC27):4C6486,113
(C3×C27)⋊5C6 = C33.5D9φ: C6/C1C6 ⊆ Aut C3×C2781(C3xC27):5C6486,162
(C3×C27)⋊6C6 = He3.5D9φ: C6/C1C6 ⊆ Aut C3×C27816+(C3xC27):6C6486,163
(C3×C27)⋊7C6 = S3×C27⋊C3φ: C6/C1C6 ⊆ Aut C3×C27546(C3xC27):7C6486,114
(C3×C27)⋊8C6 = C2×C32⋊C27φ: C6/C2C3 ⊆ Aut C3×C27162(C3xC27):8C6486,72
(C3×C27)⋊9C6 = C2×C9.5He3φ: C6/C2C3 ⊆ Aut C3×C271623(C3xC27):9C6486,79
(C3×C27)⋊10C6 = C2×C9.6He3φ: C6/C2C3 ⊆ Aut C3×C271623(C3xC27):10C6486,80
(C3×C27)⋊11C6 = C6×C27⋊C3φ: C6/C2C3 ⊆ Aut C3×C27162(C3xC27):11C6486,208
(C3×C27)⋊12C6 = C2×C27○He3φ: C6/C2C3 ⊆ Aut C3×C271623(C3xC27):12C6486,209
(C3×C27)⋊13C6 = S3×C3×C27φ: C6/C3C2 ⊆ Aut C3×C27162(C3xC27):13C6486,112
(C3×C27)⋊14C6 = C32×D27φ: C6/C3C2 ⊆ Aut C3×C27162(C3xC27):14C6486,111
(C3×C27)⋊15C6 = C3×C27⋊S3φ: C6/C3C2 ⊆ Aut C3×C27162(C3xC27):15C6486,160

Non-split extensions G=N.Q with N=C3×C27 and Q=C6
extensionφ:Q→Aut NdρLabelID
(C3×C27).C6 = C273C18φ: C6/C1C6 ⊆ Aut C3×C27546(C3xC27).C6486,15
(C3×C27).2C6 = C2×C9⋊C27φ: C6/C2C3 ⊆ Aut C3×C27486(C3xC27).2C6486,81
(C3×C27).3C6 = C2×C272C9φ: C6/C2C3 ⊆ Aut C3×C27486(C3xC27).3C6486,71
(C3×C27).4C6 = C2×C81⋊C3φ: C6/C2C3 ⊆ Aut C3×C271623(C3xC27).4C6486,84
(C3×C27).5C6 = S3×C81φ: C6/C3C2 ⊆ Aut C3×C271622(C3xC27).5C6486,33
(C3×C27).6C6 = C9×D27φ: C6/C3C2 ⊆ Aut C3×C27542(C3xC27).6C6486,13

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