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

Direct product G=N×Q with N=C23.C23 and Q=C2
dρLabelID
C2×C23.C2332C2xC2^3.C2^3128,1614

Semidirect products G=N:Q with N=C23.C23 and Q=C2
extensionφ:Q→Out NdρLabelID
C23.C231C2 = 2+ 1+44C4φ: C2/C1C2 ⊆ Out C23.C23324C2^3.C2^3:1C2128,526
C23.C232C2 = C4○D4.D4φ: C2/C1C2 ⊆ Out C23.C23168+C2^3.C2^3:2C2128,527
C23.C233C2 = (C22×Q8)⋊C4φ: C2/C1C2 ⊆ Out C23.C23328-C2^3.C2^3:3C2128,528
C23.C234C2 = M4(2)⋊19D4φ: C2/C1C2 ⊆ Out C23.C23164C2^3.C2^3:4C2128,616
C23.C235C2 = C42.5D4φ: C2/C1C2 ⊆ Out C23.C23168+C2^3.C2^3:5C2128,636
C23.C236C2 = C42.426D4φ: C2/C1C2 ⊆ Out C23.C23164C2^3.C2^3:6C2128,638
C23.C237C2 = (C2×C8)⋊4D4φ: C2/C1C2 ⊆ Out C23.C23168+C2^3.C2^3:7C2128,642
C23.C238C2 = M4(2).30D4φ: C2/C1C2 ⊆ Out C23.C23324C2^3.C2^3:8C2128,708
C23.C239C2 = M4(2)⋊5D4φ: C2/C1C2 ⊆ Out C23.C23168+C2^3.C2^3:9C2128,740
C23.C2310C2 = M4(2).D4φ: C2/C1C2 ⊆ Out C23.C23328-C2^3.C2^3:10C2128,741
C23.C2311C2 = C22⋊C4.7D4φ: C2/C1C2 ⊆ Out C23.C23324C2^3.C2^3:11C2128,785
C23.C2312C2 = C4○C2≀C4φ: C2/C1C2 ⊆ Out C23.C23164C2^3.C2^3:12C2128,852
C23.C2313C2 = C2≀C4⋊C2φ: C2/C1C2 ⊆ Out C23.C23168+C2^3.C2^3:13C2128,854
C23.C2314C2 = C4⋊Q829C4φ: C2/C1C2 ⊆ Out C23.C23164C2^3.C2^3:14C2128,858
C23.C2315C2 = C4.4D4⋊C4φ: C2/C1C2 ⊆ Out C23.C23168+C2^3.C2^3:15C2128,860
C23.C2316C2 = C23.C24φ: C2/C1C2 ⊆ Out C23.C23168+C2^3.C2^3:16C2128,1615
C23.C2317C2 = C23.4C24φ: C2/C1C2 ⊆ Out C23.C23328-C2^3.C2^3:17C2128,1616
C23.C2318C2 = C23.7C24φ: C2/C1C2 ⊆ Out C23.C23164C2^3.C2^3:18C2128,1757
C23.C2319C2 = C23.9C24φ: C2/C1C2 ⊆ Out C23.C23168+C2^3.C2^3:19C2128,1759
C23.C2320C2 = C23.10C24φ: C2/C1C2 ⊆ Out C23.C23328-C2^3.C2^3:20C2128,1760

Non-split extensions G=N.Q with N=C23.C23 and Q=C2
extensionφ:Q→Out NdρLabelID
C23.C23.1C2 = C23.2C42φ: C2/C1C2 ⊆ Out C23.C23324C2^3.C2^3.1C2128,123
C23.C23.2C2 = (C22×C8)⋊C4φ: C2/C1C2 ⊆ Out C23.C23324C2^3.C2^3.2C2128,127
C23.C23.3C2 = (C2×D4).24Q8φ: C2/C1C2 ⊆ Out C23.C23324C2^3.C2^3.3C2128,544
C23.C23.4C2 = (C2×C42)⋊C4φ: C2/C1C2 ⊆ Out C23.C23164C2^3.C2^3.4C2128,559
C23.C23.5C2 = (C2×D4).Q8φ: C2/C1C2 ⊆ Out C23.C23324C2^3.C2^3.5C2128,600
C23.C23.6C2 = C42.6D4φ: C2/C1C2 ⊆ Out C23.C23328-C2^3.C2^3.6C2128,637
C23.C23.7C2 = C4.(C4×D4)φ: C2/C1C2 ⊆ Out C23.C23328-C2^3.C2^3.7C2128,641
C23.C23.8C2 = C42.8D4φ: C2/C1C2 ⊆ Out C23.C23164C2^3.C2^3.8C2128,763
C23.C23.9C2 = C23.(C2×D4)φ: C2/C1C2 ⊆ Out C23.C23328-C2^3.C2^3.9C2128,855
C23.C23.10C2 = C4⋊Q8⋊C4φ: C2/C1C2 ⊆ Out C23.C23328-C2^3.C2^3.10C2128,861
C23.C23.11C2 = C23.5C42φ: trivial image324C2^3.C2^3.11C2128,489

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