Extensions 1→N→G→Q→1 with N=C2×He3⋊C2 and Q=C22

Direct product G=N×Q with N=C2×He3⋊C2 and Q=C22
dρLabelID
C23×He3⋊C272C2^3xHe3:C2432,561

Semidirect products G=N:Q with N=C2×He3⋊C2 and Q=C22
extensionφ:Q→Out NdρLabelID
(C2×He3⋊C2)⋊1C22 = C3⋊S3⋊D12φ: C22/C1C22 ⊆ Out C2×He3⋊C23612+(C2xHe3:C2):1C2^2432,301
(C2×He3⋊C2)⋊2C22 = C62⋊D6φ: C22/C1C22 ⊆ Out C2×He3⋊C23612+(C2xHe3:C2):2C2^2432,323
(C2×He3⋊C2)⋊3C22 = C2×He33D4φ: C22/C2C2 ⊆ Out C2×He3⋊C272(C2xHe3:C2):3C2^2432,322
(C2×He3⋊C2)⋊4C22 = C622D6φ: C22/C2C2 ⊆ Out C2×He3⋊C2366(C2xHe3:C2):4C2^2432,324
(C2×He3⋊C2)⋊5C22 = C2×He35D4φ: C22/C2C2 ⊆ Out C2×He3⋊C272(C2xHe3:C2):5C2^2432,386
(C2×He3⋊C2)⋊6C22 = D4×He3⋊C2φ: C22/C2C2 ⊆ Out C2×He3⋊C2366(C2xHe3:C2):6C2^2432,390
(C2×He3⋊C2)⋊7C22 = C2×He37D4φ: C22/C2C2 ⊆ Out C2×He3⋊C272(C2xHe3:C2):7C2^2432,399
(C2×He3⋊C2)⋊8C22 = C22×C32⋊D6φ: C22/C2C2 ⊆ Out C2×He3⋊C236(C2xHe3:C2):8C2^2432,545

Non-split extensions G=N.Q with N=C2×He3⋊C2 and Q=C22
extensionφ:Q→Out NdρLabelID
(C2×He3⋊C2).1C22 = C6.S3≀C2φ: C22/C1C22 ⊆ Out C2×He3⋊C2726-(C2xHe3:C2).1C2^2432,237
(C2×He3⋊C2).2C22 = C32⋊D6⋊C4φ: C22/C1C22 ⊆ Out C2×He3⋊C2366(C2xHe3:C2).2C2^2432,238
(C2×He3⋊C2).3C22 = C2.SU3(𝔽2)φ: C22/C1C22 ⊆ Out C2×He3⋊C2723(C2xHe3:C2).3C2^2432,239
(C2×He3⋊C2).4C22 = C12.S32φ: C22/C1C22 ⊆ Out C2×He3⋊C27212-(C2xHe3:C2).4C2^2432,299
(C2×He3⋊C2).5C22 = C62.8D6φ: C22/C1C22 ⊆ Out C2×He3⋊C27212-(C2xHe3:C2).5C2^2432,318
(C2×He3⋊C2).6C22 = C2×He3⋊D4φ: C22/C1C22 ⊆ Out C2×He3⋊C2366+(C2xHe3:C2).6C2^2432,530
(C2×He3⋊C2).7C22 = C2×SU3(𝔽2)φ: C22/C1C22 ⊆ Out C2×He3⋊C2543(C2xHe3:C2).7C2^2432,531
(C2×He3⋊C2).8C22 = C4×He3⋊C4φ: C22/C2C2 ⊆ Out C2×He3⋊C2723(C2xHe3:C2).8C2^2432,275
(C2×He3⋊C2).9C22 = C4⋊(He3⋊C4)φ: C22/C2C2 ⊆ Out C2×He3⋊C2726(C2xHe3:C2).9C2^2432,276
(C2×He3⋊C2).10C22 = C22⋊(He3⋊C4)φ: C22/C2C2 ⊆ Out C2×He3⋊C2366(C2xHe3:C2).10C2^2432,279
(C2×He3⋊C2).11C22 = C12.84S32φ: C22/C2C2 ⊆ Out C2×He3⋊C2726(C2xHe3:C2).11C2^2432,296
(C2×He3⋊C2).12C22 = C12.91S32φ: C22/C2C2 ⊆ Out C2×He3⋊C2726(C2xHe3:C2).12C2^2432,297
(C2×He3⋊C2).13C22 = C12.85S32φ: C22/C2C2 ⊆ Out C2×He3⋊C2726-(C2xHe3:C2).13C2^2432,298
(C2×He3⋊C2).14C22 = C4×C32⋊D6φ: C22/C2C2 ⊆ Out C2×He3⋊C2366(C2xHe3:C2).14C2^2432,300
(C2×He3⋊C2).15C22 = C12.86S32φ: C22/C2C2 ⊆ Out C2×He3⋊C2366+(C2xHe3:C2).15C2^2432,302
(C2×He3⋊C2).16C22 = C2×He3⋊(C2×C4)φ: C22/C2C2 ⊆ Out C2×He3⋊C272(C2xHe3:C2).16C2^2432,321
(C2×He3⋊C2).17C22 = C62.47D6φ: C22/C2C2 ⊆ Out C2×He3⋊C2726(C2xHe3:C2).17C2^2432,387
(C2×He3⋊C2).18C22 = C62.16D6φ: C22/C2C2 ⊆ Out C2×He3⋊C2726(C2xHe3:C2).18C2^2432,391
(C2×He3⋊C2).19C22 = He35D4⋊C2φ: C22/C2C2 ⊆ Out C2×He3⋊C2726(C2xHe3:C2).19C2^2432,395
(C2×He3⋊C2).20C22 = C22×He3⋊C4φ: C22/C2C2 ⊆ Out C2×He3⋊C272(C2xHe3:C2).20C2^2432,543
(C2×He3⋊C2).21C22 = C2×C4×He3⋊C2φ: trivial image72(C2xHe3:C2).21C2^2432,385
(C2×He3⋊C2).22C22 = Q8×He3⋊C2φ: trivial image726(C2xHe3:C2).22C2^2432,394

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