Large magnetoresistance and quantum oscillations in the late transition-metal compounds <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mi mathvariant="normal">I</

We synthesized high-quality single crystals of ${T}_{3}\mathrm{I}{\mathrm{n}}_{7}, T=\mathrm{Ni},\mathrm{Pd},\mathrm{Pt}$, which crystallize in a body-centered-cubic $I$m-3m space group with $T$-metal-based dumbbells. The systematic study of electrical resistivity exhibits metallic behavior with extremely large nonsaturating magnetoresistance reaching 1500% at 14 T with profound Shubnikov--de Hass quantum oscillations. The fast Fourier transformation analysis shows multiple frequencies pointing to a complex structure of the Fermi surfaces. The large magnetoresistance is attributed to the presence of small, closed Fermi surfaces with light cyclotron masses with good agreement with theoretical calculations. We present the first experimental and theoretical study of the Fermi surface in the ${T}_{3}\mathrm{I}{\mathrm{n}}_{7}$ family.