Extensions 1→N→G→Q→1 with N=C₈ and Q=C₂×Q₈

Direct product G=N×Q with N=C₈ and Q=C₂×Q₈

		d	ρ	Label	ID
Q₈×C₂×C₈		128		Q8xC2xC8	128,1690

Semidirect products G=N:Q with N=C₈ and Q=C₂×Q₈

extension	φ:Q→Aut N	d	Label	ID
C₈⋊₁(C₂×Q₈) = M₄(2)⋊₅Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	64	C8:1(C2xQ8)	128,1897
C₈⋊₂(C₂×Q₈) = D₈⋊₄Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	64	C8:2(C2xQ8)	128,2116
C₈⋊₃(C₂×Q₈) = SD₁₆⋊₂Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	64	C8:3(C2xQ8)	128,2118
C₈⋊₄(C₂×Q₈) = C₂×C₈⋊Q₈	φ: C₂×Q₈/C₂² → C₂² ⊆ Aut C₈	128	C8:4(C2xQ8)	128,1893
C₈⋊₅(C₂×Q₈) = C₂×C₈⋊₂Q₈	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	128	C8:5(C2xQ8)	128,1891
C₈⋊₆(C₂×Q₈) = C₂×C₈⋊₃Q₈	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	128	C8:6(C2xQ8)	128,1889
C₈⋊₇(C₂×Q₈) = C₂×C₈⋊₄Q₈	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	128	C8:7(C2xQ8)	128,1691
C₈⋊₈(C₂×Q₈) = Q₈×D₈	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	64	C8:8(C2xQ8)	128,2110
C₈⋊₉(C₂×Q₈) = Q₈×SD₁₆	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	64	C8:9(C2xQ8)	128,2111
C₈⋊₁₀(C₂×Q₈) = Q₈×M₄(2)	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	64	C8:10(C2xQ8)	128,1695

Non-split extensions G=N.Q with N=C₈ and Q=C₂×Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈.₁(C₂×Q₈) = D₈⋊₃Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	16	4	C8.1(C2xQ8)	128,962
C₈.₂(C₂×Q₈) = D₈.₂Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	32	4	C8.2(C2xQ8)	128,963
C₈.₃(C₂×Q₈) = M₄(2)⋊₃Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	64		C8.3(C2xQ8)	128,1895
C₈.₄(C₂×Q₈) = M₄(2)⋊₄Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	64		C8.4(C2xQ8)	128,1896
C₈.₅(C₂×Q₈) = M₄(2)⋊₆Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	64		C8.5(C2xQ8)	128,1898
C₈.₆(C₂×Q₈) = SD₁₆⋊Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	64		C8.6(C2xQ8)	128,2117
C₈.₇(C₂×Q₈) = Q₁₆⋊₄Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	128		C8.7(C2xQ8)	128,2119
C₈.₈(C₂×Q₈) = SD₁₆⋊₃Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	64		C8.8(C2xQ8)	128,2120
C₈.₉(C₂×Q₈) = D₈⋊₅Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	64		C8.9(C2xQ8)	128,2121
C₈.₁₀(C₂×Q₈) = Q₁₆⋊₅Q₈	φ: C₂×Q₈/C₄ → C₂² ⊆ Aut C₈	128		C8.10(C2xQ8)	128,2122
C₈.₁₁(C₂×Q₈) = C₂×C₈.Q₈	φ: C₂×Q₈/C₂² → C₂² ⊆ Aut C₈	32		C8.11(C2xQ8)	128,886
C₈.₁₂(C₂×Q₈) = M₅(2)⋊₃C₄	φ: C₂×Q₈/C₂² → C₂² ⊆ Aut C₈	32	4	C8.12(C2xQ8)	128,887
C₈.₁₃(C₂×Q₈) = C₄².₂₅₂D₄	φ: C₂×Q₈/C₂² → C₂² ⊆ Aut C₈	64		C8.13(C2xQ8)	128,1894
C₈.₁₄(C₂×Q₈) = C₂×C₁₆⋊₃C₄	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	128		C8.14(C2xQ8)	128,888
C₈.₁₅(C₂×Q₈) = C₂×C₁₆⋊₄C₄	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	128		C8.15(C2xQ8)	128,889
C₈.₁₆(C₂×Q₈) = C₂³.₂₅D₈	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	64		C8.16(C2xQ8)	128,890
C₈.₁₇(C₂×Q₈) = M₅(2)⋊₁C₄	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	64		C8.17(C2xQ8)	128,891
C₈.₁₈(C₂×Q₈) = C₁₆⋊₂Q₈	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	128		C8.18(C2xQ8)	128,984
C₈.₁₉(C₂×Q₈) = C₁₆.₅Q₈	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	128		C8.19(C2xQ8)	128,985
C₈.₂₀(C₂×Q₈) = C₁₆⋊₃Q₈	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	128		C8.20(C2xQ8)	128,986
C₈.₂₁(C₂×Q₈) = C₁₆⋊Q₈	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	128		C8.21(C2xQ8)	128,987
C₈.₂₂(C₂×Q₈) = C₂×C₈.₅Q₈	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	128		C8.22(C2xQ8)	128,1890
C₈.₂₃(C₂×Q₈) = C₄².₃₆₄D₄	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	64		C8.23(C2xQ8)	128,1892
C₈.₂₄(C₂×Q₈) = C₂×C₈.₄Q₈	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	64		C8.24(C2xQ8)	128,892
C₈.₂₅(C₂×Q₈) = M₅(2).₁C₄	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	32	4	C8.25(C2xQ8)	128,893
C₈.₂₆(C₂×Q₈) = C₂×C₈.C₈	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	32		C8.26(C2xQ8)	128,884
C₈.₂₇(C₂×Q₈) = M₄(2).₁C₈	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	32	4	C8.27(C2xQ8)	128,885
C₈.₂₈(C₂×Q₈) = C₄².₂₈₇C₂³	φ: C₂×Q₈/C₂×C₄ → C₂ ⊆ Aut C₈	64		C8.28(C2xQ8)	128,1693
C₈.₂₉(C₂×Q₈) = D₈⋊₁Q₈	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	64		C8.29(C2xQ8)	128,956
C₈.₃₀(C₂×Q₈) = Q₁₆⋊Q₈	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	128		C8.30(C2xQ8)	128,957
C₈.₃₁(C₂×Q₈) = D₈⋊Q₈	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	64		C8.31(C2xQ8)	128,958
C₈.₃₂(C₂×Q₈) = C₄.Q₃₂	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	128		C8.32(C2xQ8)	128,959
C₈.₃₃(C₂×Q₈) = D₈.Q₈	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	64		C8.33(C2xQ8)	128,960
C₈.₃₄(C₂×Q₈) = Q₁₆.Q₈	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	128		C8.34(C2xQ8)	128,961
C₈.₃₅(C₂×Q₈) = D₈⋊₆Q₈	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	64		C8.35(C2xQ8)	128,2112
C₈.₃₆(C₂×Q₈) = Q₈×Q₁₆	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	128		C8.36(C2xQ8)	128,2114
C₈.₃₇(C₂×Q₈) = Q₁₆⋊₆Q₈	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	128		C8.37(C2xQ8)	128,2115
C₈.₃₈(C₂×Q₈) = SD₁₆⋊₄Q₈	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	64		C8.38(C2xQ8)	128,2113
C₈.₃₉(C₂×Q₈) = M₄(2)⋊₉Q₈	φ: C₂×Q₈/Q₈ → C₂ ⊆ Aut C₈	64		C8.39(C2xQ8)	128,1694
C₈.₄₀(C₂×Q₈) = C₂×C₄⋊C₁₆	central extension (φ=1)	128		C8.40(C2xQ8)	128,881
C₈.₄₁(C₂×Q₈) = C₄⋊M₅(2)	central extension (φ=1)	64		C8.41(C2xQ8)	128,882
C₈.₄₂(C₂×Q₈) = C₄⋊C₄.₇C₈	central extension (φ=1)	64		C8.42(C2xQ8)	128,883
C₈.₄₃(C₂×Q₈) = Q₈×C₁₆	central extension (φ=1)	128		C8.43(C2xQ8)	128,914
C₈.₄₄(C₂×Q₈) = C₁₆⋊₄Q₈	central extension (φ=1)	128		C8.44(C2xQ8)	128,915
C₈.₄₅(C₂×Q₈) = C₄².₂₈₆C₂³	central extension (φ=1)	64		C8.45(C2xQ8)	128,1692

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C8 and Q=C2×Q8

Extensions 1→N→G→Q→1 with N=C₈ and Q=C₂×Q₈