Several domain-specific assistants in the form of chatbots have conquered many commercial and private areas. However, there is still a limited level of systematic knowledge of the distinctive characteristics of design elements for chatbots to facilitate development, adoption, implementation, and further research. To close this gap, the paper outlines a taxonomy of design elements for chatbots with 17 dimensions organized into the perspectives intelligence, interaction and context. The conceptually grounded design elements of the taxonomy are used to analyze 103 chatbots from 23 different application domains. Through a clustering-based approach, five chatbot archetypes that currently exist for domain-specific chatbots are identified. The developed taxonomy provides a structure to differentiate and categorize domain-specific chatbots according to archetypal qualities that guide practitioners when taking design decisions. Moreover, the taxonomy serves academics as a foundation for conducting further research on chatbot design while integrating scientific and practical knowledge.