# Extensions 1→N→G→Q→1 with N=C21 and Q=C3×C6

Direct product G=N×Q with N=C21 and Q=C3×C6
dρLabelID
C32×C42378C3^2xC42378,60

Semidirect products G=N:Q with N=C21 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
C211(C3×C6) = C3×C3⋊F7φ: C3×C6/C3C6 ⊆ Aut C21426C21:1(C3xC6)378,49
C212(C3×C6) = C32×F7φ: C3×C6/C3C6 ⊆ Aut C2163C21:2(C3xC6)378,47
C213(C3×C6) = C3×S3×C7⋊C3φ: C3×C6/C3C6 ⊆ Aut C21426C21:3(C3xC6)378,48
C214(C3×C6) = C3×C6×C7⋊C3φ: C3×C6/C6C3 ⊆ Aut C21126C21:4(C3xC6)378,52
C215(C3×C6) = C32×D21φ: C3×C6/C32C2 ⊆ Aut C21126C21:5(C3xC6)378,55
C216(C3×C6) = D7×C33φ: C3×C6/C32C2 ⊆ Aut C21189C21:6(C3xC6)378,53
C217(C3×C6) = S3×C3×C21φ: C3×C6/C32C2 ⊆ Aut C21126C21:7(C3xC6)378,54

Non-split extensions G=N.Q with N=C21 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
C21.1(C3×C6) = C9×F7φ: C3×C6/C3C6 ⊆ Aut C21636C21.1(C3xC6)378,7
C21.2(C3×C6) = C93F7φ: C3×C6/C3C6 ⊆ Aut C21636C21.2(C3xC6)378,8
C21.3(C3×C6) = C94F7φ: C3×C6/C3C6 ⊆ Aut C21636C21.3(C3xC6)378,9
C21.4(C3×C6) = C3×C7⋊C18φ: C3×C6/C3C6 ⊆ Aut C21189C21.4(C3xC6)378,10
C21.5(C3×C6) = C32.F7φ: C3×C6/C3C6 ⊆ Aut C21636C21.5(C3xC6)378,11
C21.6(C3×C6) = D7⋊He3φ: C3×C6/C3C6 ⊆ Aut C21636C21.6(C3xC6)378,12
C21.7(C3×C6) = C18×C7⋊C3φ: C3×C6/C6C3 ⊆ Aut C211263C21.7(C3xC6)378,23
C21.8(C3×C6) = C2×C63⋊C3φ: C3×C6/C6C3 ⊆ Aut C211263C21.8(C3xC6)378,24
C21.9(C3×C6) = C2×C633C3φ: C3×C6/C6C3 ⊆ Aut C211263C21.9(C3xC6)378,25
C21.10(C3×C6) = C6×C7⋊C9φ: C3×C6/C6C3 ⊆ Aut C21378C21.10(C3xC6)378,26
C21.11(C3×C6) = C2×C21.C32φ: C3×C6/C6C3 ⊆ Aut C211263C21.11(C3xC6)378,27
C21.12(C3×C6) = C2×C7⋊He3φ: C3×C6/C6C3 ⊆ Aut C211263C21.12(C3xC6)378,28
C21.13(C3×C6) = D7×C3×C9φ: C3×C6/C32C2 ⊆ Aut C21189C21.13(C3xC6)378,29
C21.14(C3×C6) = D7×He3φ: C3×C6/C32C2 ⊆ Aut C21636C21.14(C3xC6)378,30
C21.15(C3×C6) = D7×3- 1+2φ: C3×C6/C32C2 ⊆ Aut C21636C21.15(C3xC6)378,31
C21.16(C3×C6) = C14×He3central extension (φ=1)1263C21.16(C3xC6)378,45
C21.17(C3×C6) = C14×3- 1+2central extension (φ=1)1263C21.17(C3xC6)378,46

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