This article proposes to represent subgroups of finitely presented groups by their image in a quotient. It gives algorithms for basic operations in this representation and investigates how iteration of this approach can be used to extend known quotients groups with a solvable normal subgroup.
"Representing Subgroups of Finitely Presented Groups by Quotient Subgroups." Experiment. Math. 10 (3) 369 - 382, 2001.