  We study the phase diagram of the frustrated Heisenberg model on the
triangular lattice with nearest and next-nearest neighbor spin exchange
coupling, on 3-leg ladders. Using the density-matrix renormalization-group
method, we obtain the complete phase diagram of the model, which includes
quasi-long-range $120^\circ$ and columnar order, and a Majumdar-Ghosh phase
with short-ranged correlations. All these phases are non-chiral and planar. We
also identify the nature of phase transitions.
