Recently, a new group of layered transition-metal tetra-chalcogenides were proposed, via first principles calculations, to correspond to a new family of Weyl type-II semimetals with promising topological properties in the bulk as well as in the monolayer limit. In this article, we present measurements of the Shubnikov-de Haas (SdH) and de Haas-van Alphen effects under high magnetic fields for the type-II Weyl semimetallic candidate NbIrTe$_{4}$. We find that the angular dependence of the observed Fermi surface extremal cross-sectional areas agree well with our DFT calculations supporting the existence of Weyl type-II points in this material. Although we observe a large and non-saturating magnetoresistivity in NbIrTe$_{4}$ under fields all the way up to 35 T, Hall-effect measurements indicate that NbIrTe$_{4}$ is not a compensated semimetal. The transverse magnetoresistivity displays a four-fold angular dependence akin to the so-called butterfly magnetoresistivity observed in nodal line semimetals. However, we conclude that its field and this unconventional angular-dependence are governed by the topography of the Fermi-surface and the resulting anisotropy in effective masses and in carrier mobilities.
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