Studying recent adaptive radiations in isolated insular systems avoids complicating causal events and thus may offer clearer insight into mechanisms generating biological diversity. Here, we investigate evolutionary relationships and genomic differentiation within the recent radiation of Alcolapia cichlid fish that exhibit extensive phenotypic diversification, and which are confined to the extreme soda lakes Magadi and Natron in East Africa. We generated an extensive RAD data set of 96 individuals from multiple sampling sites and found evidence for genetic admixture between species within Lake Natron, with the highest levels of admixture between sympatric populations of the most recently diverged species. Despite considerable environmental separation, populations within Lake Natron do not exhibit isolation by distance, indicating panmixia within the lake, although individuals within lineages clustered by population in phylogenomic analysis. Our results indicate exceptionally low genetic differentiation across the radiation despite considerable phenotypic trophic variation, supporting previous findings from smaller data sets; however, with the increased power of densely sampled SNPs, we identify genomic peaks of differentiation (FST outliers) between Alcolapia species. While evidence of ongoing gene flow and interspecies hybridization in certain populations suggests that Alcolapia species are incompletely reproductively isolated, the identification of outlier SNPs under diversifying selection indicates the radiation is undergoing adaptive divergence.