The peak effect ͑PE͒ region in a single crystal of Ca 3 Rh 4 Sn 13 is shown to comprise two discontinuous first-order-like transitions located near its onset and peak positions, in accordance with a stepwise fracturing of the flux-line lattice. Magnetization response to thermal cycling across the onset position produces an open hysteresis loop, consistent with the notion of the fracturing. A thermomagnetic history dependence study shows that the critical current density J c (H,T) is path dependent over a large part of the (H,T) parameter space. This path dependence ceases above the peak position of the peak effect, suggesting a complete amorphization of the flux-line lattice at (T p ,H p ) line. A plausible vortex phase diagram has been constructed for Ca 3 Rh 4 Sn 13 in which phases like an elastic solid, a plastic solid, and pinned and unpinned amorphous states have been identified.