# Extensions 1→N→G→Q→1 with N=M4(2).C4 and Q=C2

Direct product G=N×Q with N=M4(2).C4 and Q=C2
dρLabelID
C2×M4(2).C432C2xM4(2).C4128,1647

Semidirect products G=N:Q with N=M4(2).C4 and Q=C2
extensionφ:Q→Out NdρLabelID
M4(2).C41C2 = M4(2).40D4φ: C2/C1C2 ⊆ Out M4(2).C4324M4(2).C4:1C2128,590
M4(2).C42C2 = M4(2).41D4φ: C2/C1C2 ⊆ Out M4(2).C4164M4(2).C4:2C2128,593
M4(2).C43C2 = C42.427D4φ: C2/C1C2 ⊆ Out M4(2).C4164M4(2).C4:3C2128,664
M4(2).C44C2 = M4(2).8D4φ: C2/C1C2 ⊆ Out M4(2).C4168+M4(2).C4:4C2128,780
M4(2).C45C2 = M4(2).9D4φ: C2/C1C2 ⊆ Out M4(2).C4328-M4(2).C4:5C2128,781
M4(2).C46C2 = C24.Q8φ: C2/C1C2 ⊆ Out M4(2).C4168+M4(2).C4:6C2128,801
M4(2).C47C2 = (C2×C8).D4φ: C2/C1C2 ⊆ Out M4(2).C4168+M4(2).C4:7C2128,813
M4(2).C48C2 = C24.11Q8φ: C2/C1C2 ⊆ Out M4(2).C4164M4(2).C4:8C2128,823
M4(2).C49C2 = C42.10D4φ: C2/C1C2 ⊆ Out M4(2).C4324M4(2).C4:9C2128,830
M4(2).C410C2 = M5(2).C22φ: C2/C1C2 ⊆ Out M4(2).C4168+M4(2).C4:10C2128,970
M4(2).C411C2 = M4(2).29C23φ: C2/C1C2 ⊆ Out M4(2).C4324M4(2).C4:11C2128,1648
M4(2).C412C2 = M4(2).51D4φ: C2/C1C2 ⊆ Out M4(2).C4164M4(2).C4:12C2128,1688
M4(2).C413C2 = M4(2).37D4φ: C2/C1C2 ⊆ Out M4(2).C4168+M4(2).C4:13C2128,1800
M4(2).C414C2 = M4(2).38D4φ: C2/C1C2 ⊆ Out M4(2).C4328-M4(2).C4:14C2128,1801
M4(2).C415C2 = C42.283C23φ: trivial image324M4(2).C4:15C2128,1687

Non-split extensions G=N.Q with N=M4(2).C4 and Q=C2
extensionφ:Q→Out NdρLabelID
M4(2).C4.1C2 = M4(2).27D4φ: C2/C1C2 ⊆ Out M4(2).C4324M4(2).C4.1C2128,685
M4(2).C4.2C2 = M4(2).15D4φ: C2/C1C2 ⊆ Out M4(2).C4328-M4(2).C4.2C2128,802
M4(2).C4.3C2 = (C2×C8).6D4φ: C2/C1C2 ⊆ Out M4(2).C4328-M4(2).C4.3C2128,814
M4(2).C4.4C2 = C42.32Q8φ: C2/C1C2 ⊆ Out M4(2).C4164M4(2).C4.4C2128,834
M4(2).C4.5C2 = C22⋊C4.Q8φ: C2/C1C2 ⊆ Out M4(2).C4324M4(2).C4.5C2128,835
M4(2).C4.6C2 = C23.10SD16φ: C2/C1C2 ⊆ Out M4(2).C4328-M4(2).C4.6C2128,971

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