Superconductivity of quasi-one-dimensional organic conductors with a quarter-filled band is investigated using the two-loop renormalization group approach to the extended Hubbard model for which both the single electron hopping t_{perp} and the repulsive interaction V_{perp} perpendicular to the chains are included. For a four-patches Fermi surface with deviations to perfect nesting, we calculate the response functions for the dominant fluctuations and possible superconducting states. By increasing V_{perp}, it is shown that a d-wave (singlet) to f-wave (triplet) superconducting state crossover occurs, and is followed by a vanishing spin gap. Furthermore, we study the influence of a magnetic field through the Zeeman coupling, from which a triplet superconducting state is found to emerge.
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