# Extensions 1→N→G→Q→1 with N=C4×He3 and Q=C22

Direct product G=N×Q with N=C4×He3 and Q=C22
dρLabelID
C22×C4×He3144C2^2xC4xHe3432,401

Semidirect products G=N:Q with N=C4×He3 and Q=C22
extensionφ:Q→Out NdρLabelID
(C4×He3)⋊1C22 = C3⋊S3⋊D12φ: C22/C1C22 ⊆ Out C4×He33612+(C4xHe3):1C2^2432,301
(C4×He3)⋊2C22 = C12.86S32φ: C22/C1C22 ⊆ Out C4×He3366+(C4xHe3):2C2^2432,302
(C4×He3)⋊3C22 = D4×C32⋊C6φ: C22/C1C22 ⊆ Out C4×He33612+(C4xHe3):3C2^2432,360
(C4×He3)⋊4C22 = D4×He3⋊C2φ: C22/C1C22 ⊆ Out C4×He3366(C4xHe3):4C2^2432,390
(C4×He3)⋊5C22 = C4×C32⋊D6φ: C22/C1C22 ⊆ Out C4×He3366(C4xHe3):5C2^2432,300
(C4×He3)⋊6C22 = C2×He34D4φ: C22/C2C2 ⊆ Out C4×He372(C4xHe3):6C2^2432,350
(C4×He3)⋊7C22 = C2×He35D4φ: C22/C2C2 ⊆ Out C4×He372(C4xHe3):7C2^2432,386
(C4×He3)⋊8C22 = C2×C4×C32⋊C6φ: C22/C2C2 ⊆ Out C4×He372(C4xHe3):8C2^2432,349
(C4×He3)⋊9C22 = C2×C4×He3⋊C2φ: C22/C2C2 ⊆ Out C4×He372(C4xHe3):9C2^2432,385
(C4×He3)⋊10C22 = C2×D4×He3φ: C22/C2C2 ⊆ Out C4×He372(C4xHe3):10C2^2432,404

Non-split extensions G=N.Q with N=C4×He3 and Q=C22
extensionφ:Q→Out NdρLabelID
(C4×He3).1C22 = He33SD16φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).1C2^2432,78
(C4×He3).2C22 = He32D8φ: C22/C1C22 ⊆ Out C4×He3726+(C4xHe3).2C2^2432,79
(C4×He3).3C22 = He32Q16φ: C22/C1C22 ⊆ Out C4×He31446-(C4xHe3).3C2^2432,80
(C4×He3).4C22 = He33D8φ: C22/C1C22 ⊆ Out C4×He37212+(C4xHe3).4C2^2432,83
(C4×He3).5C22 = He34SD16φ: C22/C1C22 ⊆ Out C4×He37212-(C4xHe3).5C2^2432,84
(C4×He3).6C22 = He35SD16φ: C22/C1C22 ⊆ Out C4×He37212+(C4xHe3).6C2^2432,85
(C4×He3).7C22 = He33Q16φ: C22/C1C22 ⊆ Out C4×He314412-(C4xHe3).7C2^2432,86
(C4×He3).8C22 = He38SD16φ: C22/C1C22 ⊆ Out C4×He37212-(C4xHe3).8C2^2432,152
(C4×He3).9C22 = He36D8φ: C22/C1C22 ⊆ Out C4×He37212+(C4xHe3).9C2^2432,153
(C4×He3).10C22 = He36Q16φ: C22/C1C22 ⊆ Out C4×He314412-(C4xHe3).10C2^2432,160
(C4×He3).11C22 = He310SD16φ: C22/C1C22 ⊆ Out C4×He37212+(C4xHe3).11C2^2432,161
(C4×He3).12C22 = He37D8φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).12C2^2432,192
(C4×He3).13C22 = He39SD16φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).13C2^2432,193
(C4×He3).14C22 = He311SD16φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).14C2^2432,196
(C4×He3).15C22 = He37Q16φ: C22/C1C22 ⊆ Out C4×He31446(C4xHe3).15C2^2432,197
(C4×He3).16C22 = C3⋊S3⋊Dic6φ: C22/C1C22 ⊆ Out C4×He37212-(C4xHe3).16C2^2432,294
(C4×He3).17C22 = C12⋊S3⋊S3φ: C22/C1C22 ⊆ Out C4×He37212+(C4xHe3).17C2^2432,295
(C4×He3).18C22 = C12.84S32φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).18C2^2432,296
(C4×He3).19C22 = C12.85S32φ: C22/C1C22 ⊆ Out C4×He3726-(C4xHe3).19C2^2432,298
(C4×He3).20C22 = C12.S32φ: C22/C1C22 ⊆ Out C4×He37212-(C4xHe3).20C2^2432,299
(C4×He3).21C22 = C62.13D6φ: C22/C1C22 ⊆ Out C4×He37212-(C4xHe3).21C2^2432,361
(C4×He3).22C22 = Q8×C32⋊C6φ: C22/C1C22 ⊆ Out C4×He37212-(C4xHe3).22C2^2432,368
(C4×He3).23C22 = (Q8×He3)⋊C2φ: C22/C1C22 ⊆ Out C4×He37212+(C4xHe3).23C2^2432,369
(C4×He3).24C22 = C62.16D6φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).24C2^2432,391
(C4×He3).25C22 = Q8×He3⋊C2φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).25C2^2432,394
(C4×He3).26C22 = He35D4⋊C2φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).26C2^2432,395
(C4×He3).27C22 = C32⋊C6⋊C8φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).27C2^2432,76
(C4×He3).28C22 = He3⋊M4(2)φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).28C2^2432,77
(C4×He3).29C22 = C12.89S32φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).29C2^2432,81
(C4×He3).30C22 = He33M4(2)φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).30C2^2432,82
(C4×He3).31C22 = C12.91S32φ: C22/C1C22 ⊆ Out C4×He3726(C4xHe3).31C2^2432,297
(C4×He3).32C22 = He34Q16φ: C22/C2C2 ⊆ Out C4×He31446-(C4xHe3).32C2^2432,114
(C4×He3).33C22 = He36SD16φ: C22/C2C2 ⊆ Out C4×He3726(C4xHe3).33C2^2432,117
(C4×He3).34C22 = He34D8φ: C22/C2C2 ⊆ Out C4×He3726+(C4xHe3).34C2^2432,118
(C4×He3).35C22 = He37SD16φ: C22/C2C2 ⊆ Out C4×He3726(C4xHe3).35C2^2432,175
(C4×He3).36C22 = He35D8φ: C22/C2C2 ⊆ Out C4×He3726(C4xHe3).36C2^2432,176
(C4×He3).37C22 = He35Q16φ: C22/C2C2 ⊆ Out C4×He31446(C4xHe3).37C2^2432,177
(C4×He3).38C22 = C2×He33Q8φ: C22/C2C2 ⊆ Out C4×He3144(C4xHe3).38C2^2432,348
(C4×He3).39C22 = C2×He34Q8φ: C22/C2C2 ⊆ Out C4×He3144(C4xHe3).39C2^2432,384
(C4×He3).40C22 = C62.47D6φ: C22/C2C2 ⊆ Out C4×He3726(C4xHe3).40C2^2432,387
(C4×He3).41C22 = C8×C32⋊C6φ: C22/C2C2 ⊆ Out C4×He3726(C4xHe3).41C2^2432,115
(C4×He3).42C22 = He35M4(2)φ: C22/C2C2 ⊆ Out C4×He3726(C4xHe3).42C2^2432,116
(C4×He3).43C22 = C2×He33C8φ: C22/C2C2 ⊆ Out C4×He3144(C4xHe3).43C2^2432,136
(C4×He3).44C22 = He37M4(2)φ: C22/C2C2 ⊆ Out C4×He3726(C4xHe3).44C2^2432,137
(C4×He3).45C22 = C8×He3⋊C2φ: C22/C2C2 ⊆ Out C4×He3723(C4xHe3).45C2^2432,173
(C4×He3).46C22 = He36M4(2)φ: C22/C2C2 ⊆ Out C4×He3726(C4xHe3).46C2^2432,174
(C4×He3).47C22 = C2×He34C8φ: C22/C2C2 ⊆ Out C4×He3144(C4xHe3).47C2^2432,184
(C4×He3).48C22 = He38M4(2)φ: C22/C2C2 ⊆ Out C4×He3726(C4xHe3).48C2^2432,185
(C4×He3).49C22 = C62.36D6φ: C22/C2C2 ⊆ Out C4×He3726(C4xHe3).49C2^2432,351
(C4×He3).50C22 = D8×He3φ: C22/C2C2 ⊆ Out C4×He3726(C4xHe3).50C2^2432,216
(C4×He3).51C22 = SD16×He3φ: C22/C2C2 ⊆ Out C4×He3726(C4xHe3).51C2^2432,219
(C4×He3).52C22 = Q16×He3φ: C22/C2C2 ⊆ Out C4×He31446(C4xHe3).52C2^2432,222
(C4×He3).53C22 = C2×Q8×He3φ: C22/C2C2 ⊆ Out C4×He3144(C4xHe3).53C2^2432,407
(C4×He3).54C22 = C2×C8×He3φ: trivial image144(C4xHe3).54C2^2432,210
(C4×He3).55C22 = M4(2)×He3φ: trivial image726(C4xHe3).55C2^2432,213
(C4×He3).56C22 = C4○D4×He3φ: trivial image726(C4xHe3).56C2^2432,410

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