# Extensions 1→N→G→Q→1 with N=C2×He3 and Q=C23

Direct product G=N×Q with N=C2×He3 and Q=C23
dρLabelID
C24×He3144C2^4xHe3432,563

Semidirect products G=N:Q with N=C2×He3 and Q=C23
extensionφ:Q→Out NdρLabelID
(C2×He3)⋊C23 = C22×C32⋊D6φ: C23/C2C22 ⊆ Out C2×He336(C2xHe3):C2^3432,545
(C2×He3)⋊2C23 = C23×C32⋊C6φ: C23/C22C2 ⊆ Out C2×He372(C2xHe3):2C2^3432,558
(C2×He3)⋊3C23 = C23×He3⋊C2φ: C23/C22C2 ⊆ Out C2×He372(C2xHe3):3C2^3432,561

Non-split extensions G=N.Q with N=C2×He3 and Q=C23
extensionφ:Q→Out NdρLabelID
(C2×He3).1C23 = C3⋊S3⋊Dic6φ: C23/C2C22 ⊆ Out C2×He37212-(C2xHe3).1C2^3432,294
(C2×He3).2C23 = C12⋊S3⋊S3φ: C23/C2C22 ⊆ Out C2×He37212+(C2xHe3).2C2^3432,295
(C2×He3).3C23 = C12.84S32φ: C23/C2C22 ⊆ Out C2×He3726(C2xHe3).3C2^3432,296
(C2×He3).4C23 = C12.91S32φ: C23/C2C22 ⊆ Out C2×He3726(C2xHe3).4C2^3432,297
(C2×He3).5C23 = C12.85S32φ: C23/C2C22 ⊆ Out C2×He3726-(C2xHe3).5C2^3432,298
(C2×He3).6C23 = C12.S32φ: C23/C2C22 ⊆ Out C2×He37212-(C2xHe3).6C2^3432,299
(C2×He3).7C23 = C4×C32⋊D6φ: C23/C2C22 ⊆ Out C2×He3366(C2xHe3).7C2^3432,300
(C2×He3).8C23 = C3⋊S3⋊D12φ: C23/C2C22 ⊆ Out C2×He33612+(C2xHe3).8C2^3432,301
(C2×He3).9C23 = C12.86S32φ: C23/C2C22 ⊆ Out C2×He3366+(C2xHe3).9C2^3432,302
(C2×He3).10C23 = C2×He32Q8φ: C23/C2C22 ⊆ Out C2×He3144(C2xHe3).10C2^3432,316
(C2×He3).11C23 = C2×C6.S32φ: C23/C2C22 ⊆ Out C2×He372(C2xHe3).11C2^3432,317
(C2×He3).12C23 = C62.8D6φ: C23/C2C22 ⊆ Out C2×He37212-(C2xHe3).12C2^3432,318
(C2×He3).13C23 = C62.9D6φ: C23/C2C22 ⊆ Out C2×He3726(C2xHe3).13C2^3432,319
(C2×He3).14C23 = C2×He32D4φ: C23/C2C22 ⊆ Out C2×He372(C2xHe3).14C2^3432,320
(C2×He3).15C23 = C2×He3⋊(C2×C4)φ: C23/C2C22 ⊆ Out C2×He372(C2xHe3).15C2^3432,321
(C2×He3).16C23 = C2×He33D4φ: C23/C2C22 ⊆ Out C2×He372(C2xHe3).16C2^3432,322
(C2×He3).17C23 = C62⋊D6φ: C23/C2C22 ⊆ Out C2×He33612+(C2xHe3).17C2^3432,323
(C2×He3).18C23 = C622D6φ: C23/C2C22 ⊆ Out C2×He3366(C2xHe3).18C2^3432,324
(C2×He3).19C23 = C2×He33Q8φ: C23/C22C2 ⊆ Out C2×He3144(C2xHe3).19C2^3432,348
(C2×He3).20C23 = C2×C4×C32⋊C6φ: C23/C22C2 ⊆ Out C2×He372(C2xHe3).20C2^3432,349
(C2×He3).21C23 = C2×He34D4φ: C23/C22C2 ⊆ Out C2×He372(C2xHe3).21C2^3432,350
(C2×He3).22C23 = C62.36D6φ: C23/C22C2 ⊆ Out C2×He3726(C2xHe3).22C2^3432,351
(C2×He3).23C23 = D4×C32⋊C6φ: C23/C22C2 ⊆ Out C2×He33612+(C2xHe3).23C2^3432,360
(C2×He3).24C23 = C62.13D6φ: C23/C22C2 ⊆ Out C2×He37212-(C2xHe3).24C2^3432,361
(C2×He3).25C23 = Q8×C32⋊C6φ: C23/C22C2 ⊆ Out C2×He37212-(C2xHe3).25C2^3432,368
(C2×He3).26C23 = (Q8×He3)⋊C2φ: C23/C22C2 ⊆ Out C2×He37212+(C2xHe3).26C2^3432,369
(C2×He3).27C23 = C22×C32⋊C12φ: C23/C22C2 ⊆ Out C2×He3144(C2xHe3).27C2^3432,376
(C2×He3).28C23 = C2×He36D4φ: C23/C22C2 ⊆ Out C2×He372(C2xHe3).28C2^3432,377
(C2×He3).29C23 = C2×He34Q8φ: C23/C22C2 ⊆ Out C2×He3144(C2xHe3).29C2^3432,384
(C2×He3).30C23 = C2×C4×He3⋊C2φ: C23/C22C2 ⊆ Out C2×He372(C2xHe3).30C2^3432,385
(C2×He3).31C23 = C2×He35D4φ: C23/C22C2 ⊆ Out C2×He372(C2xHe3).31C2^3432,386
(C2×He3).32C23 = C62.47D6φ: C23/C22C2 ⊆ Out C2×He3726(C2xHe3).32C2^3432,387
(C2×He3).33C23 = D4×He3⋊C2φ: C23/C22C2 ⊆ Out C2×He3366(C2xHe3).33C2^3432,390
(C2×He3).34C23 = C62.16D6φ: C23/C22C2 ⊆ Out C2×He3726(C2xHe3).34C2^3432,391
(C2×He3).35C23 = Q8×He3⋊C2φ: C23/C22C2 ⊆ Out C2×He3726(C2xHe3).35C2^3432,394
(C2×He3).36C23 = He35D4⋊C2φ: C23/C22C2 ⊆ Out C2×He3726(C2xHe3).36C2^3432,395
(C2×He3).37C23 = C22×He33C4φ: C23/C22C2 ⊆ Out C2×He3144(C2xHe3).37C2^3432,398
(C2×He3).38C23 = C2×He37D4φ: C23/C22C2 ⊆ Out C2×He372(C2xHe3).38C2^3432,399
(C2×He3).39C23 = C22×C4×He3φ: trivial image144(C2xHe3).39C2^3432,401
(C2×He3).40C23 = C2×D4×He3φ: trivial image72(C2xHe3).40C2^3432,404
(C2×He3).41C23 = C2×Q8×He3φ: trivial image144(C2xHe3).41C2^3432,407
(C2×He3).42C23 = C4○D4×He3φ: trivial image726(C2xHe3).42C2^3432,410

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