# Extensions 1→N→G→Q→1 with N=C3×C6 and Q=C22

Direct product G=N×Q with N=C3×C6 and Q=C22
dρLabelID
C2×C6272C2xC6^272,50

Semidirect products G=N:Q with N=C3×C6 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊C22 = C2×S32φ: C22/C1C22 ⊆ Aut C3×C6124+(C3xC6):C2^272,46
(C3×C6)⋊2C22 = S3×C2×C6φ: C22/C2C2 ⊆ Aut C3×C624(C3xC6):2C2^272,48
(C3×C6)⋊3C22 = C22×C3⋊S3φ: C22/C2C2 ⊆ Aut C3×C636(C3xC6):3C2^272,49

Non-split extensions G=N.Q with N=C3×C6 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C3×C6).1C22 = S3×Dic3φ: C22/C1C22 ⊆ Aut C3×C6244-(C3xC6).1C2^272,20
(C3×C6).2C22 = C6.D6φ: C22/C1C22 ⊆ Aut C3×C6124+(C3xC6).2C2^272,21
(C3×C6).3C22 = D6⋊S3φ: C22/C1C22 ⊆ Aut C3×C6244-(C3xC6).3C2^272,22
(C3×C6).4C22 = C3⋊D12φ: C22/C1C22 ⊆ Aut C3×C6124+(C3xC6).4C2^272,23
(C3×C6).5C22 = C322Q8φ: C22/C1C22 ⊆ Aut C3×C6244-(C3xC6).5C2^272,24
(C3×C6).6C22 = C3×Dic6φ: C22/C2C2 ⊆ Aut C3×C6242(C3xC6).6C2^272,26
(C3×C6).7C22 = S3×C12φ: C22/C2C2 ⊆ Aut C3×C6242(C3xC6).7C2^272,27
(C3×C6).8C22 = C3×D12φ: C22/C2C2 ⊆ Aut C3×C6242(C3xC6).8C2^272,28
(C3×C6).9C22 = C6×Dic3φ: C22/C2C2 ⊆ Aut C3×C624(C3xC6).9C2^272,29
(C3×C6).10C22 = C3×C3⋊D4φ: C22/C2C2 ⊆ Aut C3×C6122(C3xC6).10C2^272,30
(C3×C6).11C22 = C324Q8φ: C22/C2C2 ⊆ Aut C3×C672(C3xC6).11C2^272,31
(C3×C6).12C22 = C4×C3⋊S3φ: C22/C2C2 ⊆ Aut C3×C636(C3xC6).12C2^272,32
(C3×C6).13C22 = C12⋊S3φ: C22/C2C2 ⊆ Aut C3×C636(C3xC6).13C2^272,33
(C3×C6).14C22 = C2×C3⋊Dic3φ: C22/C2C2 ⊆ Aut C3×C672(C3xC6).14C2^272,34
(C3×C6).15C22 = C327D4φ: C22/C2C2 ⊆ Aut C3×C636(C3xC6).15C2^272,35
(C3×C6).16C22 = D4×C32central extension (φ=1)36(C3xC6).16C2^272,37
(C3×C6).17C22 = Q8×C32central extension (φ=1)72(C3xC6).17C2^272,38

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