We report on the results of a de Haas-van Alphen (dHvA) measurement performed on the recently discovered antiferromagnet URhIn$_5$ ($T_N$ = 98 K), a 5textit{f}-analogue of the well studied heavy fermion antiferromagnet CeRhIn$_5$. The Fermi surface is found to consist of four surfaces: a roughly spherical pocket $beta$, with $F_beta simeq 0.3$ kT; a pillow-shaped closed surface, $alpha$, with $F_alpha simeq 1.1$ kT; and two higher frequencies $gamma_1$ with $F_{gamma_1} simeq 3.2$ kT and $gamma_2$ with $F_{gamma_2} simeq 3.5$ kT that are seen only near the textit{c}-axis, and that may arise on cylindrical Fermi surfaces. The measured cyclotron masses range from 1.9 $m_e$ to 4.3 $m_e$. A simple LDA+SO calculation performed for the paramagnetic ground state shows a very different Fermi surface topology, demonstrating a need for more advanced electronic structure calculations.
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