The Jesuits do not have a female religious component in the Society. However, there are a number of congregations of women religious that have modeled themselves on Ignatian spirituality, such as the Congregation of the Sisters of St. Joseph, the Handmaids of the Sacred Heart of Jesus, etc.
General Congregation 34 launched a small scale project into a third order type relationship, but at General Congregation 35, the project ended (See GC35 Decree 6, Paragraph 58). The Jesuits do have many lay partners that are integral in numerous Jesuits works such as Apostleship of Prayer, Christian Life Communities, Jesuit Volunteer Corps, Ignatian Volunteer Corps, among others (
source).