Mixed anomalies and generalized symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories (QFTs). A natural question is whether these are related in any way to certain supersymmetric partition functions or indices, which have also been used extensively to study the dynamics of QFTs. In this talk, we address this question in the context of 3d N≥3 gauge theories using the superconformal index. In particular, using the index we are able to detect mixed anomalies involving discrete 0-form global symmetries, and possibly a 1-form symmetry. The effectiveness of this method is demonstrated via several classes of theories, including Chern-Simons-matter theories, the T(SU(N)) theory of Gaiotto-Witten and variants of the Aharony-Bergman-Jafferis (ABJ) theory with the orthosymplectic gauge algebra. Gauging appropriate global symmetries involved in mixed anomalies of some of these models and using constructions available in the literature, we obtain various interesting theories with two-group structures or non-invertible symmetries.