  The Peak Effect (PE) regime in a single crystal of Ca$_3$Rh$_4$Sn$_{13}$ has
been investigated in detail via ac susceptibility as well as dc magnetization
measurements. The PE region comprises two discontinuous first order like
transitions, located near its onset and peak positions and reflects a stepwise
fracturing of the flux line lattice (FLL). This scenario can be construed as an
alternative to a scheme involving the appearance of Generalized
Fulde-Ferrel-Larkin-Ovchinnikov (GFFLO) state as considered in the case of PE
phenomenon in isostructural Yb$_3$Rh$_4$Sn$_{13}$ system. The procedure of
thermal cycling across the onset position of PE produces an open hysteresis
loop, which is consistent with the notion of the fracturing of the FLL. A study
of thermomagnetic history dependence of different metastable vortex states
shows the path dependence in the critical current density J_c(H,T) over a large
part of the (H,T) parameter space. The path dependence in J_c ceases above the
peak position of the PE, suggesting a complete amorphization and the loss of
long range correlations of the FLL at (T_p, H_p) line. A plausible vortex phase
diagram has been illustrated for Ca$_3$Rh$_4$Sn$_{13}$n and phases like an
elastic solid, a plastic solid, a pinned amorphous and an unpinned amorphous
states have been identified.
