# Extensions 1→N→G→Q→1 with N=C4⋊(C32⋊C4) and Q=C2

Direct product G=N×Q with N=C4⋊(C32⋊C4) and Q=C2
dρLabelID
C2×C4⋊(C32⋊C4)48C2xC4:(C3^2:C4)288,933

Semidirect products G=N:Q with N=C4⋊(C32⋊C4) and Q=C2
extensionφ:Q→Out NdρLabelID
C4⋊(C32⋊C4)⋊1C2 = C3⋊S3.2D8φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)244C4:(C3^2:C4):1C2288,377
C4⋊(C32⋊C4)⋊2C2 = C3⋊S3.5D8φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)248+C4:(C3^2:C4):2C2288,430
C4⋊(C32⋊C4)⋊3C2 = S32⋊Q8φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)244C4:(C3^2:C4):3C2288,868
C4⋊(C32⋊C4)⋊4C2 = S32⋊D4φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)244C4:(C3^2:C4):4C2288,878
C4⋊(C32⋊C4)⋊5C2 = D4×C32⋊C4φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)248+C4:(C3^2:C4):5C2288,936
C4⋊(C32⋊C4)⋊6C2 = (C6×C12)⋊5C4φ: trivial image244C4:(C3^2:C4):6C2288,934

Non-split extensions G=N.Q with N=C4⋊(C32⋊C4) and Q=C2
extensionφ:Q→Out NdρLabelID
C4⋊(C32⋊C4).1C2 = C3⋊S3.2Q16φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)484C4:(C3^2:C4).1C2288,378
C4⋊(C32⋊C4).2C2 = C3⋊S3.5Q16φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)488-C4:(C3^2:C4).2C2288,432
C4⋊(C32⋊C4).3C2 = Q8×C32⋊C4φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)488-C4:(C3^2:C4).3C2288,938
C4⋊(C32⋊C4).4C2 = C4.PSU3(𝔽2)φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)488C4:(C3^2:C4).4C2288,393
C4⋊(C32⋊C4).5C2 = C4.2PSU3(𝔽2)φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)488C4:(C3^2:C4).5C2288,394
C4⋊(C32⋊C4).6C2 = C8⋊(C32⋊C4)φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)484C4:(C3^2:C4).6C2288,416
C4⋊(C32⋊C4).7C2 = C3⋊S3.4D8φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)484C4:(C3^2:C4).7C2288,417
C4⋊(C32⋊C4).8C2 = C4.3PSU3(𝔽2)φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)488C4:(C3^2:C4).8C2288,891
C4⋊(C32⋊C4).9C2 = C4⋊PSU3(𝔽2)φ: C2/C1C2 ⊆ Out C4⋊(C32⋊C4)368C4:(C3^2:C4).9C2288,893

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