We present an analysis of the decays B{0}-->K{*0}(892)gamma and B{+}-->K{*+}(892)gamma using a sample of about 383 x 10{6} BB[-over ] events collected with the BABAR detector at the PEP-II asymmetric energy B factory. We measure the branching fractions B(B{0}-->K{*0}gamma)=(4.47+/-0.10+/-0.16) x 10{-5} and B(B{+}-->K{*+}gamma)=(4.22+/-0.14+/-0.16) x 10{-5}. We constrain the direct CP asymmetry to be -0.033<A(B-->K{*}gamma)<0.028 and the isospin asymmetry to be 0.017<Delta{0-} < 0.116, where the limits are determined by the 90% confidence interval and include both the statistical and systematic uncertainties.