Summary: When \(1\to H\to G\to Q\to 1\) is a short exact sequence of three word-hyperbolic groups, Mahan Mj (formerly Mitra) [M. Mitra, Topology 37, No. 3, 527–538 (1998; Zbl 0907.20038)] has shown that the inclusion map from \(H\) to \(G\) extends continuously to a map between the Gromov boundaries of \(H\) and \(G\). This boundary map is known as the Cannon-Thurston map. In this context, Mj associates to every point \(z\) in the Gromov boundary of \(Q\) an “ending lamination” on \(H\) which consists of pairs of distinct points in the boundary of \(H\). We prove that for each such \(z\), the quotient of the Gromov boundary of \(H\) by the equivalence relation generated by this ending lamination is a dendrite, that is, a tree-like topological space. This result generalizes the work of I. Kapovich and M. Lustig [J. Lond. Math. Soc., II. Ser. 91, No. 1, 203–224 (2015; Zbl 1325.20035)] and S. Dowdall et al. [Isr. J. Math. 216, No. 2, 753–797 (2016; Zbl 1361.20030)], who prove that in the case where \(H\) is a free group and \(Q\) is a convex cocompact purely atoroidal subgroup of \(\mathrm{Out}(F_N)\), one can identify the resultant quotient space with a certain \(\mathbb{R}\)-tree in the boundary of Culler and Vogtmann’s Outer space.