The purpose of this paper is to describe the construction of a supervisory control system for telemanipulation of a robotic hand with a Data Glove. This system aims to establish interaction control such as preshaping, grasping, and orienting operations. The system consists of a Data Glove as a master device, as well as slave controllers and a slave robot. The feedback loop of the slave system is closed at the slave side so that the slave controllers manipulate an object stably following commands from a Data Glove. A Data Glove usually extracts a subject's hand shape in order to map it to a slave hand. However, the proposed method only extracts a few key pieces of information which slave controllers require. We explain the proposed system and propose a way to extract the key information with a Data Glove. An experiment is executed to validate the proposed method.