Extensions 1→N→G→Q→1 with N=C₄ and Q=Q₈×D₇

Direct product G=N×Q with N=C₄ and Q=Q₈×D₇

		d	ρ	Label	ID
C₄×Q₈×D₇		224		C4xQ8xD7	448,1024

Semidirect products G=N:Q with N=C₄ and Q=Q₈×D₇

extension	φ:Q→Aut N	d	Label	ID
C₄⋊₁(Q₈×D₇) = D₂₈⋊₈Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	224	C4:1(Q8xD7)	448,1180
C₄⋊₂(Q₈×D₇) = D₇×C₄⋊Q₈	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	224	C4:2(Q8xD7)	448,1176
C₄⋊₃(Q₈×D₇) = Q₈×D₂₈	φ: Q₈×D₇/C₇×Q₈ → C₂ ⊆ Aut C₄	224	C4:3(Q8xD7)	448,1028

Non-split extensions G=N.Q with N=C₄ and Q=Q₈×D₇

extension	φ:Q→Aut N	d	Label	ID
C₄.₁(Q₈×D₇) = Dic₁₄⋊Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	448	C4.1(Q8xD7)	448,388
C₄.₂(Q₈×D₇) = Dic₁₄.Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	448	C4.2(Q8xD7)	448,391
C₄.₃(Q₈×D₇) = D₂₈⋊Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	224	C4.3(Q8xD7)	448,404
C₄.₄(Q₈×D₇) = D₂₈.Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	224	C4.4(Q8xD7)	448,405
C₄.₅(Q₈×D₇) = Dic₁₄⋊₂Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	448	C4.5(Q8xD7)	448,409
C₄.₆(Q₈×D₇) = Dic₁₄.₂Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	448	C4.6(Q8xD7)	448,411
C₄.₇(Q₈×D₇) = D₂₈⋊₂Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	224	C4.7(Q8xD7)	448,424
C₄.₈(Q₈×D₇) = D₂₈.₂Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	224	C4.8(Q8xD7)	448,425
C₄.₉(Q₈×D₇) = Dic₁₄.₄Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	448	C4.9(Q8xD7)	448,597
C₄.₁₀(Q₈×D₇) = D₂₈.₄Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	224	C4.10(Q8xD7)	448,600
C₄.₁₁(Q₈×D₇) = D₂₈⋊₅Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	224	C4.11(Q8xD7)	448,618
C₄.₁₂(Q₈×D₇) = D₂₈⋊₆Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	224	C4.12(Q8xD7)	448,621
C₄.₁₃(Q₈×D₇) = Dic₁₄⋊₅Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	448	C4.13(Q8xD7)	448,625
C₄.₁₄(Q₈×D₇) = Dic₁₄⋊₆Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	448	C4.14(Q8xD7)	448,628
C₄.₁₅(Q₈×D₇) = Dic₁₄⋊₇Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	448	C4.15(Q8xD7)	448,1138
C₄.₁₆(Q₈×D₇) = D₂₈⋊₇Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	224	C4.16(Q8xD7)	448,1143
C₄.₁₇(Q₈×D₇) = Dic₁₄⋊₈Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	448	C4.17(Q8xD7)	448,1174
C₄.₁₈(Q₈×D₇) = Dic₁₄⋊₉Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	448	C4.18(Q8xD7)	448,1175
C₄.₁₉(Q₈×D₇) = D₂₈⋊₉Q₈	φ: Q₈×D₇/Dic₁₄ → C₂ ⊆ Aut C₄	224	C4.19(Q8xD7)	448,1183
C₄.₂₀(Q₈×D₇) = C₅₆⋊₅Q₈	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	448	C4.20(Q8xD7)	448,389
C₄.₂₁(Q₈×D₇) = C₅₆⋊₃Q₈	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	448	C4.21(Q8xD7)	448,390
C₄.₂₂(Q₈×D₇) = C₅₆.₈Q₈	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	448	C4.22(Q8xD7)	448,392
C₄.₂₃(Q₈×D₇) = D₇×C₄.Q₈	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	224	C4.23(Q8xD7)	448,393
C₄.₂₄(Q₈×D₇) = (C₈×D₇)⋊C₄	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	224	C4.24(Q8xD7)	448,394
C₄.₂₅(Q₈×D₇) = C₈⋊(C₄×D₇)	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	224	C4.25(Q8xD7)	448,395
C₄.₂₆(Q₈×D₇) = C₅₆⋊₂Q₈	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	448	C4.26(Q8xD7)	448,408
C₄.₂₇(Q₈×D₇) = C₅₆⋊₄Q₈	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	448	C4.27(Q8xD7)	448,410
C₄.₂₈(Q₈×D₇) = C₅₆.₄Q₈	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	448	C4.28(Q8xD7)	448,412
C₄.₂₉(Q₈×D₇) = D₇×C₂.D₈	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	224	C4.29(Q8xD7)	448,413
C₄.₃₀(Q₈×D₇) = C₈.₂₇(C₄×D₇)	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	224	C4.30(Q8xD7)	448,414
C₄.₃₁(Q₈×D₇) = C₅₆⋊(C₂×C₄)	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	224	C4.31(Q8xD7)	448,415
C₄.₃₂(Q₈×D₇) = C₄².₂₁₅D₁₄	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	448	C4.32(Q8xD7)	448,598
C₄.₃₃(Q₈×D₇) = C₄².₆₈D₁₄	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	448	C4.33(Q8xD7)	448,599
C₄.₃₄(Q₈×D₇) = C₂₈.₁₇D₈	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	448	C4.34(Q8xD7)	448,612
C₄.₃₅(Q₈×D₇) = C₂₈.SD₁₆	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	448	C4.35(Q8xD7)	448,613
C₄.₃₆(Q₈×D₇) = C₄².₇₆D₁₄	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	448	C4.36(Q8xD7)	448,614
C₄.₃₇(Q₈×D₇) = D₇×C₄².C₂	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	224	C4.37(Q8xD7)	448,1140
C₄.₃₈(Q₈×D₇) = C₄².₂₃₆D₁₄	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	224	C4.38(Q8xD7)	448,1141
C₄.₃₉(Q₈×D₇) = C₄².₁₄₈D₁₄	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	224	C4.39(Q8xD7)	448,1142
C₄.₄₀(Q₈×D₇) = C₄².₂₄₁D₁₄	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	224	C4.40(Q8xD7)	448,1181
C₄.₄₁(Q₈×D₇) = C₄².₁₇₄D₁₄	φ: Q₈×D₇/C₄×D₇ → C₂ ⊆ Aut C₄	224	C4.41(Q8xD7)	448,1182
C₄.₄₂(Q₈×D₇) = Dic₁₄.₃Q₈	φ: Q₈×D₇/C₇×Q₈ → C₂ ⊆ Aut C₄	448	C4.42(Q8xD7)	448,363
C₄.₄₃(Q₈×D₇) = D₂₈⋊₃Q₈	φ: Q₈×D₇/C₇×Q₈ → C₂ ⊆ Aut C₄	224	C4.43(Q8xD7)	448,376
C₄.₄₄(Q₈×D₇) = D₂₈⋊₄Q₈	φ: Q₈×D₇/C₇×Q₈ → C₂ ⊆ Aut C₄	224	C4.44(Q8xD7)	448,380
C₄.₄₅(Q₈×D₇) = D₂₈.₃Q₈	φ: Q₈×D₇/C₇×Q₈ → C₂ ⊆ Aut C₄	224	C4.45(Q8xD7)	448,381
C₄.₄₆(Q₈×D₇) = C₂₈.₇Q₁₆	φ: Q₈×D₇/C₇×Q₈ → C₂ ⊆ Aut C₄	448	C4.46(Q8xD7)	448,384
C₄.₄₇(Q₈×D₇) = Dic₁₄⋊₄Q₈	φ: Q₈×D₇/C₇×Q₈ → C₂ ⊆ Aut C₄	448	C4.47(Q8xD7)	448,385
C₄.₄₈(Q₈×D₇) = Q₈×Dic₁₄	φ: Q₈×D₇/C₇×Q₈ → C₂ ⊆ Aut C₄	448	C4.48(Q8xD7)	448,1019
C₄.₄₉(Q₈×D₇) = Dic₁₄⋊₁₀Q₈	φ: Q₈×D₇/C₇×Q₈ → C₂ ⊆ Aut C₄	448	C4.49(Q8xD7)	448,1020
C₄.₅₀(Q₈×D₇) = D₂₈⋊₁₀Q₈	φ: Q₈×D₇/C₇×Q₈ → C₂ ⊆ Aut C₄	224	C4.50(Q8xD7)	448,1032
C₄.₅₁(Q₈×D₇) = C₄².₂₇D₁₄	central extension (φ=1)	448	C4.51(Q8xD7)	448,362
C₄.₅₂(Q₈×D₇) = Dic₁₄⋊C₈	central extension (φ=1)	448	C4.52(Q8xD7)	448,364
C₄.₅₃(Q₈×D₇) = C₂₈.M₄(2)	central extension (φ=1)	448	C4.53(Q8xD7)	448,365
C₄.₅₄(Q₈×D₇) = D₇×C₄⋊C₈	central extension (φ=1)	224	C4.54(Q8xD7)	448,366
C₄.₅₅(Q₈×D₇) = C₂₈⋊M₄(2)	central extension (φ=1)	224	C4.55(Q8xD7)	448,371
C₄.₅₆(Q₈×D₇) = C₄².₃₀D₁₄	central extension (φ=1)	224	C4.56(Q8xD7)	448,373
C₄.₅₇(Q₈×D₇) = Q₈×C₇⋊C₈	central extension (φ=1)	448	C4.57(Q8xD7)	448,557
C₄.₅₈(Q₈×D₇) = C₄².₂₁₀D₁₄	central extension (φ=1)	448	C4.58(Q8xD7)	448,558
C₄.₅₉(Q₈×D₇) = C₄².₂₃₂D₁₄	central extension (φ=1)	224	C4.59(Q8xD7)	448,1031

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C4 and Q=Q8×D7

Extensions 1→N→G→Q→1 with N=C₄ and Q=Q₈×D₇