  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.
