  Since very few Type-I superconductors are known and most are elemental
superconductors, there are very few experimental platforms where the
interaction between Type-I superconductivity and topologically nontrivial band
structure can be probed. The rhenium aluminide Al$_6$Re has recently been
identified as a Type-I superconductor with a transition of 0.74\,K and a
critical field of $\sim$50\,Oe. Here, we report its magnetotransport behavior
including de Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillations.
Angular dependence of the magnetoresistance reveals a highly anisotropic Fermi
surface with dominant hole character. From the strong oscillatory component
$\Delta R_{xx}$ in high magnetic fields up to 33\,T, the Landau index
infinite-field intercept in the case of a single oscillation frequency, and the
phase factor $\varphi$ where multiple frequencies coexist, are both $\sim$1/4.
This intermediate value is suggestive of possible nontrivial band topology but
does not allow strong conclusions.
