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

Direct product G=N×Q with N=C4×He3 and Q=C4
dρLabelID
C42×He3144C4^2xHe3432,201

Semidirect products G=N:Q with N=C4×He3 and Q=C4
extensionφ:Q→Out NdρLabelID
(C4×He3)⋊1C4 = C4×He3⋊C4φ: C4/C1C4 ⊆ Out C4×He3723(C4xHe3):1C4432,275
(C4×He3)⋊2C4 = C4⋊(He3⋊C4)φ: C4/C1C4 ⊆ Out C4×He3726(C4xHe3):2C4432,276
(C4×He3)⋊3C4 = C62.20D6φ: C4/C2C2 ⊆ Out C4×He3144(C4xHe3):3C4432,140
(C4×He3)⋊4C4 = C62.30D6φ: C4/C2C2 ⊆ Out C4×He3144(C4xHe3):4C4432,188
(C4×He3)⋊5C4 = C4×C32⋊C12φ: C4/C2C2 ⊆ Out C4×He3144(C4xHe3):5C4432,138
(C4×He3)⋊6C4 = C4×He33C4φ: C4/C2C2 ⊆ Out C4×He3144(C4xHe3):6C4432,186
(C4×He3)⋊7C4 = C4⋊C4×He3φ: C4/C2C2 ⊆ Out C4×He3144(C4xHe3):7C4432,207

Non-split extensions G=N.Q with N=C4×He3 and Q=C4
extensionφ:Q→Out NdρLabelID
(C4×He3).1C4 = He32C16φ: C4/C1C4 ⊆ Out C4×He31443(C4xHe3).1C4432,57
(C4×He3).2C4 = He32(C2×C8)φ: C4/C1C4 ⊆ Out C4×He3723(C4xHe3).2C4432,273
(C4×He3).3C4 = He31M4(2)φ: C4/C1C4 ⊆ Out C4×He3726(C4xHe3).3C4432,274
(C4×He3).4C4 = He37M4(2)φ: C4/C2C2 ⊆ Out C4×He3726(C4xHe3).4C4432,137
(C4×He3).5C4 = He38M4(2)φ: C4/C2C2 ⊆ Out C4×He3726(C4xHe3).5C4432,185
(C4×He3).6C4 = He33C16φ: C4/C2C2 ⊆ Out C4×He31446(C4xHe3).6C4432,30
(C4×He3).7C4 = He34C16φ: C4/C2C2 ⊆ Out C4×He31443(C4xHe3).7C4432,33
(C4×He3).8C4 = C2×He33C8φ: C4/C2C2 ⊆ Out C4×He3144(C4xHe3).8C4432,136
(C4×He3).9C4 = C2×He34C8φ: C4/C2C2 ⊆ Out C4×He3144(C4xHe3).9C4432,184
(C4×He3).10C4 = M4(2)×He3φ: C4/C2C2 ⊆ Out C4×He3726(C4xHe3).10C4432,213
(C4×He3).11C4 = C16×He3φ: trivial image1443(C4xHe3).11C4432,35
(C4×He3).12C4 = C2×C8×He3φ: trivial image144(C4xHe3).12C4432,210

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