Based on a sample of $2.25\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{8}J/\\ensuremath{\\psi}$ events taken with the BESIII detector at the BEPCII collider, we present the results of a study of the decay $J/\\ensuremath{\\psi}\\ensuremath{\\rightarrow}\\ensuremath{\\eta}\\ensuremath{\\phi}{\\ensuremath{\\pi}}^{+}{\\ensuremath{\\pi}}^{\\ensuremath{-}}$. The $Y(2175)$ resonance is observed in the invariant mass spectrum of $\\ensuremath{\\phi}{f}_{0}(980)$ with a statistical significance of greater than $10\\ensuremath{\\sigma}$. The corresponding mass and width are determined to be $M=2200\\ifmmode\\pm\\else\\textpm\\fi{}6(\\mathrm{stat})\\ifmmode\\pm\\else\\textpm\\fi{}5(\\mathrm{syst})\\text{ }\\text{ }\\mathrm{MeV}/{c}^{2}$ and $\\mathrm{\\ensuremath{\\Gamma}}=104\\ifmmode\\pm\\else\\textpm\\fi{}15(\\mathrm{stat})\\ifmmode\\pm\\else\\textpm\\fi{}\\phantom{\\rule{0ex}{0ex}}15(\\mathrm{syst})\\text{ }\\text{ }\\mathrm{MeV}$, respectively, and the product branching fraction is measured to be $\\mathcal{B}(J/\\ensuremath{\\psi}\\ensuremath{\\rightarrow}\\ensuremath{\\eta}Y(2175),\\phantom{\\rule{0ex}{0ex}}Y(2175)\\ensuremath{\\rightarrow}\\ensuremath{\\phi}{f}_{0}(980),{f}_{0}(980)\\ensuremath{\\rightarrow}{\\ensuremath{\\pi}}^{+}{\\ensuremath{\\pi}}^{\\ensuremath{-}})=(1.20\\ifmmode\\pm\\else\\textpm\\fi{}0.14(\\mathrm{stat})\\ifmmode\\pm\\else\\textpm\\fi{}0.37(\\mathrm{syst}))\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}4}$. The results are consistent within errors with those of previous experiments. We also measure the branching fraction of $J/\\ensuremath{\\psi}\\ensuremath{\\rightarrow}\\ensuremath{\\phi}{f}_{1}(1285)$ with ${f}_{1}(1285)\\ensuremath{\\rightarrow}\\ensuremath{\\eta}{\\ensuremath{\\pi}}^{+}{\\ensuremath{\\pi}}^{\\ensuremath{-}}$ and set upper limits on the branching fractions for $J/\\ensuremath{\\psi}\\ensuremath{\\rightarrow}\\ensuremath{\\phi}\\ensuremath{\\eta}(1405)/\\ensuremath{\\phi}X(1835)/\\ensuremath{\\phi}X(1870)$ with $\\ensuremath{\\eta}(1405)/X(1835)/X(1870)\\ensuremath{\\rightarrow}\\ensuremath{\\eta}{\\ensuremath{\\pi}}^{+}{\\ensuremath{\\pi}}^{\\ensuremath{-}}$ at the 90% confidence level.