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The massive amount of genomic data appearing for SARS-CoV-2 since the beginning of the COVID-19 pandemic has challenged traditional methods for studying its dynamics. As a result, new methods such as Pangolin, which can scale to the millions of samples of SARS-CoV-2 currently available, have appeared. Such a tool is tailored to take as input assembled, aligned and curated full-length sequences, such as those found in the GISAID database. As high-throughput sequencing technologies continue to advance, such assembly, alignment and curation may become a bottleneck, creating a need for methods which can process raw sequencing reads directly. In this paper, we propose Reads2Vec, an alignment-free embedding approach that can generate a fixed-length feature vector representation directly from the raw sequencing reads without requiring assembly. Furthermore, since such an embedding is a numerical representation, it may be applied to highly optimized classification and clustering algorithms. Experiments on simulated data show that our proposed embedding obtains better classification results and better clustering properties contrary to existing alignment-free baselines. In a study on real data, we show that alignment-free embeddings have better clustering properties than the Pangolin tool and that the spike region of the SARS-CoV-2 genome heavily informs the alignment-free clusterings, which is consistent with current biological knowledge of SARS-CoV-2.