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Extensions 1→N→G→Q→1 with N=C2×C56 and Q=C4

Direct product G=N×Q with N=C2×C56 and Q=C4
dρLabelID
C2×C4×C56448C2xC4xC56448,810

Semidirect products G=N:Q with N=C2×C56 and Q=C4
extensionφ:Q→Aut NdρLabelID
(C2×C56)⋊1C4 = (C2×C56)⋊C4φ: C4/C1 → C4 ⊆ Aut C2×C561124(C2xC56):1C4448,113
(C2×C56)⋊2C4 = C23.9D28φ: C4/C1 → C4 ⊆ Aut C2×C561124(C2xC56):2C4448,114
(C2×C56)⋊3C4 = C7×C4.9C42φ: C4/C1 → C4 ⊆ Aut C2×C561124(C2xC56):3C4448,141
(C2×C56)⋊4C4 = C7×M4(2)⋊4C4φ: C4/C1 → C4 ⊆ Aut C2×C561124(C2xC56):4C4448,148
(C2×C56)⋊5C4 = (C2×C56)⋊5C4φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56):5C4448,107
(C2×C56)⋊6C4 = C28.9C42φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56):6C4448,108
(C2×C56)⋊7C4 = C7×C22.7C42φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56):7C4448,140
(C2×C56)⋊8C4 = C7×C22.4Q16φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56):8C4448,144
(C2×C56)⋊9C4 = C2×C56⋊1C4φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56):9C4448,639
(C2×C56)⋊10C4 = C23.22D28φ: C4/C2 → C2 ⊆ Aut C2×C56224(C2xC56):10C4448,640
(C2×C56)⋊11C4 = C2×C8⋊Dic7φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56):11C4448,638
(C2×C56)⋊12C4 = C2×C8×Dic7φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56):12C4448,632
(C2×C56)⋊13C4 = C2×C56⋊C4φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56):13C4448,634
(C2×C56)⋊14C4 = C28.12C42φ: C4/C2 → C2 ⊆ Aut C2×C56224(C2xC56):14C4448,635
(C2×C56)⋊15C4 = C14×C2.D8φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56):15C4448,834
(C2×C56)⋊16C4 = C7×C23.25D4φ: C4/C2 → C2 ⊆ Aut C2×C56224(C2xC56):16C4448,835
(C2×C56)⋊17C4 = C14×C4.Q8φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56):17C4448,833
(C2×C56)⋊18C4 = C14×C8⋊C4φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56):18C4448,811
(C2×C56)⋊19C4 = C7×C8○2M4(2)φ: C4/C2 → C2 ⊆ Aut C2×C56224(C2xC56):19C4448,813

Non-split extensions G=N.Q with N=C2×C56 and Q=C4
extensionφ:Q→Aut NdρLabelID
(C2×C56).1C4 = C28.15C42φ: C4/C1 → C4 ⊆ Aut C2×C561124(C2xC56).1C4448,23
(C2×C56).2C4 = C56.D4φ: C4/C1 → C4 ⊆ Aut C2×C561124(C2xC56).2C4448,110
(C2×C56).3C4 = C28.21C42φ: C4/C1 → C4 ⊆ Aut C2×C561124(C2xC56).3C4448,117
(C2×C56).4C4 = C7×C4.10C42φ: C4/C1 → C4 ⊆ Aut C2×C561124(C2xC56).4C4448,142
(C2×C56).5C4 = C7×C16⋊C4φ: C4/C1 → C4 ⊆ Aut C2×C561124(C2xC56).5C4448,151
(C2×C56).6C4 = C7×C23.C8φ: C4/C1 → C4 ⊆ Aut C2×C561124(C2xC56).6C4448,153
(C2×C56).7C4 = C42.279D14φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).7C4448,11
(C2×C56).8C4 = C56⋊2C8φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).8C4448,14
(C2×C56).9C4 = C56⋊1C8φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).9C4448,15
(C2×C56).10C4 = C28⋊C16φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).10C4448,19
(C2×C56).11C4 = C56.91D4φ: C4/C2 → C2 ⊆ Aut C2×C56224(C2xC56).11C4448,106
(C2×C56).12C4 = C28.10C42φ: C4/C2 → C2 ⊆ Aut C2×C56224(C2xC56).12C4448,109
(C2×C56).13C4 = C7×C8⋊2C8φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).13C4448,138
(C2×C56).14C4 = C7×C8⋊1C8φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).14C4448,139
(C2×C56).15C4 = C7×C4.C42φ: C4/C2 → C2 ⊆ Aut C2×C56224(C2xC56).15C4448,145
(C2×C56).16C4 = C7×C22⋊C16φ: C4/C2 → C2 ⊆ Aut C2×C56224(C2xC56).16C4448,152
(C2×C56).17C4 = C7×C4⋊C16φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).17C4448,167
(C2×C56).18C4 = C56.16Q8φ: C4/C2 → C2 ⊆ Aut C2×C561122(C2xC56).18C4448,20
(C2×C56).19C4 = C2×C56.C4φ: C4/C2 → C2 ⊆ Aut C2×C56224(C2xC56).19C4448,641
(C2×C56).20C4 = C8×C7⋊C8φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).20C4448,10
(C2×C56).21C4 = C56⋊C8φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).21C4448,12
(C2×C56).22C4 = C4×C7⋊C16φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).22C4448,17
(C2×C56).23C4 = C56.C8φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).23C4448,18
(C2×C56).24C4 = C2×C7⋊C32φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).24C4448,55
(C2×C56).25C4 = C7⋊M6(2)φ: C4/C2 → C2 ⊆ Aut C2×C562242(C2xC56).25C4448,56
(C2×C56).26C4 = C22×C7⋊C16φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).26C4448,630
(C2×C56).27C4 = C2×C28.C8φ: C4/C2 → C2 ⊆ Aut C2×C56224(C2xC56).27C4448,631
(C2×C56).28C4 = C7×C8.C8φ: C4/C2 → C2 ⊆ Aut C2×C561122(C2xC56).28C4448,168
(C2×C56).29C4 = C14×C8.C4φ: C4/C2 → C2 ⊆ Aut C2×C56224(C2xC56).29C4448,837
(C2×C56).30C4 = C7×C8⋊C8φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).30C4448,126
(C2×C56).31C4 = C7×C16⋊5C4φ: C4/C2 → C2 ⊆ Aut C2×C56448(C2xC56).31C4448,150
(C2×C56).32C4 = C7×M6(2)φ: C4/C2 → C2 ⊆ Aut C2×C562242(C2xC56).32C4448,174
(C2×C56).33C4 = C14×M5(2)φ: C4/C2 → C2 ⊆ Aut C2×C56224(C2xC56).33C4448,911

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