Extensions 1→N→G→Q→1 with N=C₅₆ and Q=C₂xC₄

Direct product G=NxQ with N=C₅₆ and Q=C₂xC₄

		d	ρ	Label	ID
C₂xC₄xC₅₆		448		C2xC4xC56	448,810

Semidirect products G=N:Q with N=C₅₆ and Q=C₂xC₄

extension	φ:Q→Aut N	d	Label	ID
C₅₆:₁(C₂xC₄) = C₄².₁₆D₁₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:1(C2xC4)	448,244
C₅₆:₂(C₂xC₄) = D₅₆:C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:2(C2xC4)	448,245
C₅₆:₃(C₂xC₄) = C₂³.₄₇D₂₈	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:3(C2xC4)	448,655
C₅₆:₄(C₂xC₄) = Dic₇:₅D₈	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:4(C2xC4)	448,406
C₅₆:₅(C₂xC₄) = D₇xC₂.D₈	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:5(C2xC4)	448,413
C₅₆:₆(C₂xC₄) = D₈xDic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:6(C2xC4)	448,683
C₅₆:₇(C₂xC₄) = C₈:(C₄xD₇)	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:7(C2xC4)	448,395
C₅₆:₈(C₂xC₄) = D₅₆:₉C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:8(C2xC4)	448,403
C₅₆:₉(C₂xC₄) = SD₁₆:Dic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:9(C2xC4)	448,698
C₅₆:₁₀(C₂xC₄) = C₅₆:(C₂xC₄)	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:10(C2xC4)	448,415
C₅₆:₁₁(C₂xC₄) = C₅₆:C₂:C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:11(C2xC4)	448,423
C₅₆:₁₂(C₂xC₄) = D₈:Dic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:12(C2xC4)	448,686
C₅₆:₁₃(C₂xC₄) = Dic₇:₈SD₁₆	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:13(C2xC4)	448,386
C₅₆:₁₄(C₂xC₄) = D₇xC₄.Q₈	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:14(C2xC4)	448,393
C₅₆:₁₅(C₂xC₄) = SD₁₆xDic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:15(C2xC4)	448,695
C₅₆:₁₆(C₂xC₄) = D₇xC₈:C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:16(C2xC4)	448,238
C₅₆:₁₇(C₂xC₄) = Dic₇.C₄²	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:17(C2xC4)	448,241
C₅₆:₁₈(C₂xC₄) = M₄(2)xDic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:18(C2xC4)	448,651
C₅₆:₁₉(C₂xC₄) = C₇xM₄(2):C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:19(C2xC4)	448,836
C₅₆:₂₀(C₂xC₄) = C₇xSD₁₆:C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:20(C2xC4)	448,848
C₅₆:₂₁(C₂xC₄) = C₇xD₈:C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	C56:21(C2xC4)	448,850
C₅₆:₂₂(C₂xC₄) = C₄xD₅₆	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	C56:22(C2xC4)	448,226
C₅₆:₂₃(C₂xC₄) = C₄xC₅₆:C₂	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	C56:23(C2xC4)	448,225
C₅₆:₂₄(C₂xC₄) = D₇xC₄xC₈	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	C56:24(C2xC4)	448,218
C₅₆:₂₅(C₂xC₄) = C₄xC₈:D₇	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	C56:25(C2xC4)	448,221
C₅₆:₂₆(C₂xC₄) = D₈xC₂₈	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	C56:26(C2xC4)	448,845
C₅₆:₂₇(C₂xC₄) = SD₁₆xC₂₈	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	C56:27(C2xC4)	448,846
C₅₆:₂₈(C₂xC₄) = M₄(2)xC₂₈	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	C56:28(C2xC4)	448,812
C₅₆:₂₉(C₂xC₄) = C₂xC₅₆:₁C₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448	C56:29(C2xC4)	448,639
C₅₆:₃₀(C₂xC₄) = C₂xC₈:Dic₇	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448	C56:30(C2xC4)	448,638
C₅₆:₃₁(C₂xC₄) = C₂xC₈xDic₇	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448	C56:31(C2xC4)	448,632
C₅₆:₃₂(C₂xC₄) = C₂xC₅₆:C₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448	C56:32(C2xC4)	448,634
C₅₆:₃₃(C₂xC₄) = C₁₄xC₂.D₈	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448	C56:33(C2xC4)	448,834
C₅₆:₃₄(C₂xC₄) = C₁₄xC₄.Q₈	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448	C56:34(C2xC4)	448,833
C₅₆:₃₅(C₂xC₄) = C₁₄xC₈:C₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448	C56:35(C2xC4)	448,811

Non-split extensions G=N.Q with N=C₅₆ and Q=C₂xC₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆.₁(C₂xC₄) = C₂₈.₃D₈	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4+	C56.1(C2xC4)	448,73
C₅₆.₂(C₂xC₄) = C₂₈.₄D₈	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	4-	C56.2(C2xC4)	448,74
C₅₆.₃(C₂xC₄) = D₅₆:₂C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.3(C2xC4)	448,75
C₅₆.₄(C₂xC₄) = Dic₂₈:C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	448		C56.4(C2xC4)	448,250
C₅₆.₅(C₂xC₄) = D₅₆:₄C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.5(C2xC4)	448,251
C₅₆.₆(C₂xC₄) = M₄(2).Dic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.6(C2xC4)	448,659
C₅₆.₇(C₂xC₄) = C₈.₄Dic₁₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	448		C56.7(C2xC4)	448,46
C₅₆.₈(C₂xC₄) = C₈.₅Dic₁₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	448		C56.8(C2xC4)	448,47
C₅₆.₉(C₂xC₄) = C₁₄.D₁₆	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224		C56.9(C2xC4)	448,48
C₅₆.₁₀(C₂xC₄) = C₅₆.₆D₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	448		C56.10(C2xC4)	448,49
C₅₆.₁₁(C₂xC₄) = C₈.₇Dic₁₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	4	C56.11(C2xC4)	448,50
C₅₆.₁₂(C₂xC₄) = Dic₂₈.C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	4	C56.12(C2xC4)	448,54
C₅₆.₁₃(C₂xC₄) = C₁₄.SD₃₂	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224		C56.13(C2xC4)	448,119
C₅₆.₁₄(C₂xC₄) = C₁₄.Q₃₂	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	448		C56.14(C2xC4)	448,121
C₅₆.₁₅(C₂xC₄) = C₂₈.₅₈D₈	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	4	C56.15(C2xC4)	448,124
C₅₆.₁₆(C₂xC₄) = Dic₂₈:₆C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	448		C56.16(C2xC4)	448,407
C₅₆.₁₇(C₂xC₄) = C₈.₂₇(C₄xD₇)	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224		C56.17(C2xC4)	448,414
C₅₆.₁₈(C₂xC₄) = D₇xC₈.C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.18(C2xC4)	448,426
C₅₆.₁₉(C₂xC₄) = Q₁₆xDic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	448		C56.19(C2xC4)	448,717
C₅₆.₂₀(C₂xC₄) = D₈:₅Dic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.20(C2xC4)	448,730
C₅₆.₂₁(C₂xC₄) = D₅₆:₈C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.21(C2xC4)	448,45
C₅₆.₂₂(C₂xC₄) = D₅₆.C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4+	C56.22(C2xC4)	448,52
C₅₆.₂₃(C₂xC₄) = C₅₆.₈D₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	4-	C56.23(C2xC4)	448,53
C₅₆.₂₄(C₂xC₄) = Dic₂₈:₉C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	448		C56.24(C2xC4)	448,387
C₅₆.₂₅(C₂xC₄) = D₈.Dic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.25(C2xC4)	448,120
C₅₆.₂₆(C₂xC₄) = Q₁₆.Dic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	4	C56.26(C2xC4)	448,122
C₅₆.₂₇(C₂xC₄) = D₈:₂Dic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.27(C2xC4)	448,123
C₅₆.₂₈(C₂xC₄) = M₄(2).₂₅D₁₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.28(C2xC4)	448,427
C₅₆.₂₉(C₂xC₄) = D₅₆:₁₀C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.29(C2xC4)	448,428
C₅₆.₃₀(C₂xC₄) = Q₁₆:Dic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	448		C56.30(C2xC4)	448,718
C₅₆.₃₁(C₂xC₄) = D₈:₄Dic₇	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.31(C2xC4)	448,731
C₅₆.₃₂(C₂xC₄) = C₅₆.Q₈	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.32(C2xC4)	448,44
C₅₆.₃₃(C₂xC₄) = C₈.Dic₁₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.33(C2xC4)	448,51
C₅₆.₃₄(C₂xC₄) = (C₈xD₇):C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224		C56.34(C2xC4)	448,394
C₅₆.₃₅(C₂xC₄) = D₅₆:₇C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.35(C2xC4)	448,429
C₅₆.₃₆(C₂xC₄) = C₂₈.₁₅C₄²	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.36(C2xC4)	448,23
C₅₆.₃₇(C₂xC₄) = D₁₄.₄C₄²	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224		C56.37(C2xC4)	448,242
C₅₆.₃₈(C₂xC₄) = D₇xM₅(2)	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.38(C2xC4)	448,440
C₅₆.₃₉(C₂xC₄) = C₁₆.₁₂D₁₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	4	C56.39(C2xC4)	448,441
C₅₆.₄₀(C₂xC₄) = C₂₈.₇C₄²	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224		C56.40(C2xC4)	448,656
C₅₆.₄₁(C₂xC₄) = C₅₆.₇₀C₂³	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	4	C56.41(C2xC4)	448,674
C₅₆.₄₂(C₂xC₄) = C₇xD₈:₂C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.42(C2xC4)	448,164
C₅₆.₄₃(C₂xC₄) = C₇xM₅(2):C₂	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.43(C2xC4)	448,165
C₅₆.₄₄(C₂xC₄) = C₇xC₈.₁₇D₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	224	4	C56.44(C2xC4)	448,166
C₅₆.₄₅(C₂xC₄) = C₇xM₄(2).C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.45(C2xC4)	448,838
C₅₆.₄₆(C₂xC₄) = C₇xQ₁₆:C₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	448		C56.46(C2xC4)	448,849
C₅₆.₄₇(C₂xC₄) = C₇xC₈.₂₆D₄	φ: C₂xC₄/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.47(C2xC4)	448,852
C₅₆.₄₈(C₂xC₄) = C₅₆.₇₈D₄	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	448		C56.48(C2xC4)	448,60
C₅₆.₄₉(C₂xC₄) = C₂.D₁₁₂	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224		C56.49(C2xC4)	448,66
C₅₆.₅₀(C₂xC₄) = D₅₆.₁C₄	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	2	C56.50(C2xC4)	448,67
C₅₆.₅₁(C₂xC₄) = C₄xDic₂₈	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	448		C56.51(C2xC4)	448,232
C₅₆.₅₂(C₂xC₄) = D₅₆:₁₁C₄	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	112	2	C56.52(C2xC4)	448,234
C₅₆.₅₃(C₂xC₄) = D₇xC₃₂	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	2	C56.53(C2xC4)	448,3
C₅₆.₅₄(C₂xC₄) = C₃₂:D₇	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	2	C56.54(C2xC4)	448,4
C₅₆.₅₅(C₂xC₄) = C₄xC₇:C₁₆	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	448		C56.55(C2xC4)	448,17
C₅₆.₅₆(C₂xC₄) = C₅₆.C₈	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	448		C56.56(C2xC4)	448,18
C₅₆.₅₇(C₂xC₄) = C₁₆xDic₇	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	448		C56.57(C2xC4)	448,57
C₅₆.₅₈(C₂xC₄) = C₁₁₂:₉C₄	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	448		C56.58(C2xC4)	448,59
C₅₆.₅₉(C₂xC₄) = D₁₄.C₄²	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224		C56.59(C2xC4)	448,223
C₅₆.₆₀(C₂xC₄) = D₇xC₂xC₁₆	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224		C56.60(C2xC4)	448,433
C₅₆.₆₁(C₂xC₄) = C₂xC₁₆:D₇	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224		C56.61(C2xC4)	448,434
C₅₆.₆₂(C₂xC₄) = D₂₈.₄C₈	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	2	C56.62(C2xC4)	448,435
C₅₆.₆₃(C₂xC₄) = C₇xC₂.D₁₆	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224		C56.63(C2xC4)	448,161
C₅₆.₆₄(C₂xC₄) = C₇xC₂.Q₃₂	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	448		C56.64(C2xC4)	448,162
C₅₆.₆₅(C₂xC₄) = C₇xD₈.C₄	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	2	C56.65(C2xC4)	448,163
C₅₆.₆₆(C₂xC₄) = Q₁₆xC₂₈	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	448		C56.66(C2xC4)	448,847
C₅₆.₆₇(C₂xC₄) = C₇xC₈oD₈	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	112	2	C56.67(C2xC4)	448,851
C₅₆.₆₈(C₂xC₄) = C₇xD₄oC₁₆	φ: C₂xC₄/C₄ → C₂ ⊆ Aut C₅₆	224	2	C56.68(C2xC4)	448,912
C₅₆.₆₉(C₂xC₄) = C₁₁₂:₅C₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448		C56.69(C2xC4)	448,61
C₅₆.₇₀(C₂xC₄) = C₁₁₂:₆C₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448		C56.70(C2xC4)	448,62
C₅₆.₇₁(C₂xC₄) = C₁₁₂.C₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	224	2	C56.71(C2xC4)	448,63
C₅₆.₇₂(C₂xC₄) = C₁₆:Dic₇	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	112	4	C56.72(C2xC4)	448,70
C₅₆.₇₃(C₂xC₄) = C₂³.₂₂D₂₈	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	224		C56.73(C2xC4)	448,640
C₅₆.₇₄(C₂xC₄) = C₂xC₅₆.C₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	224		C56.74(C2xC4)	448,641
C₅₆.₇₅(C₂xC₄) = C₂xC₇:C₃₂	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448		C56.75(C2xC4)	448,55
C₅₆.₇₆(C₂xC₄) = C₇:M₆(2)	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	224	2	C56.76(C2xC4)	448,56
C₅₆.₇₇(C₂xC₄) = C₁₁₂:C₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	112	4	C56.77(C2xC4)	448,69
C₅₆.₇₈(C₂xC₄) = C₂²xC₇:C₁₆	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448		C56.78(C2xC4)	448,630
C₅₆.₇₉(C₂xC₄) = C₂xC₂₈.C₈	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	224		C56.79(C2xC4)	448,631
C₅₆.₈₀(C₂xC₄) = C₂₈.₁₂C₄²	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	224		C56.80(C2xC4)	448,635
C₅₆.₈₁(C₂xC₄) = C₇xC₁₆:₃C₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448		C56.81(C2xC4)	448,170
C₅₆.₈₂(C₂xC₄) = C₇xC₁₆:₄C₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	448		C56.82(C2xC4)	448,171
C₅₆.₈₃(C₂xC₄) = C₇xC₈.₄Q₈	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	224	2	C56.83(C2xC4)	448,172
C₅₆.₈₄(C₂xC₄) = C₇xC₂³.₂₅D₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	224		C56.84(C2xC4)	448,835
C₅₆.₈₅(C₂xC₄) = C₁₄xC₈.C₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	224		C56.85(C2xC4)	448,837
C₅₆.₈₆(C₂xC₄) = C₇xC₈.Q₈	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	112	4	C56.86(C2xC4)	448,169
C₅₆.₈₇(C₂xC₄) = C₇xC₁₆:C₄	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	112	4	C56.87(C2xC4)	448,151
C₅₆.₈₈(C₂xC₄) = C₇xC₈o₂M₄(2)	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	224		C56.88(C2xC4)	448,813
C₅₆.₈₉(C₂xC₄) = C₁₄xM₅(2)	φ: C₂xC₄/C₂² → C₂ ⊆ Aut C₅₆	224		C56.89(C2xC4)	448,911
C₅₆.₉₀(C₂xC₄) = C₇xC₁₆:₅C₄	central extension (φ=1)	448		C56.90(C2xC4)	448,150
C₅₆.₉₁(C₂xC₄) = C₇xM₆(2)	central extension (φ=1)	224	2	C56.91(C2xC4)	448,174

Extensions 1→N→G→Q→1 with N=C56 and Q=C2xC4

Extensions 1→N→G→Q→1 with N=C₅₆ and Q=C₂xC₄