The transport and thermodynamic properties of $beta$-ReO$_{2}$ crystallizing in a nonsymmorphic structure were studied using high-quality single crystals. An extremely large magnetoresistance (XMR) reaching 22,000 $%$ in a transverse magnetic field of 10 T at 2 K was observed. However, distinguished from other topological semimetals with low carrier densities that show XMR, $beta$-ReO$_{2}$ has a high electron carrier density of 1 $times$ $10^{22}$ cm$^{-3}$ as determined by Hall measurements and large Fermi surfaces in the electronic structure. In addition, a small Fermi surface with a small effective mass was evidenced by de Haas-van Alphen oscillation measurements. The previous band structure calculations [S. S. Wang, et al., Nat. Commun. 8, 1844 (2017)] showed that two kinds of loops made of Dirac points of hourglass-shaped dispersions exist and are connected to each other by a point to form a string of alternating loops, called the Dirac loop chain (DLC), which are protected by the multiple glide symmetries. Our first-principles calculations revealed the complex Fermi surfaces with the smallest one corresponding to the observed small Fermi surface, which is just located near the DLC. The XMR of $beta$-ReO$_{2}$ is attributed to the small Fermi surface and thus is likely caused by the DLC.
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