To manage the scale and complexity of 6G autonomous network deployments, the concept of intent-driven networking has been introduced. Intents are further autonomously handled by implementations of intent management functions. The scalable management of intents is foreseen to be hierarchical, with multiple intent management functions at the business, management and resource levels. This hierarchy brings in challenges in decomposing high-level intent expectations to sub-intents to be solved by lower-level intent managers. In this paper, we present DETROIT, a framework for hierarchical intent decomposition. In DETROIT, we examine the use of multiple decomposition algorithms to determine the optimal decomposition techniques. To provide correct decompositions, a QoS algebraic formulation is incorporated within the decomposition algorithms. Intent reports are further composed to provide feedback on the efficacy of the decomposition process. Further prediction and evaluation steps ensure careful deliberation of the outputs before actuation. The decomposition is implemented over a network slicing use case with multiple expectations. We demonstrate that through the use of the agents and QoS algebra proposed within DETROIT, the decomposed targets are generated within 2% deviation. This process further captures the tradeoff between reaching intent expectation targets and resource optimality. Such an automated process of intent decomposition would be crucial in a hierarchy of 6G intent management functions.