We　consider　a　Newton-CG　augmented　Lagrangian　method　for　solving　semidefinite　programming　(SDP)　problems　from　the　perspective　of　approximate　semismooth　Newton　methods.　In　order　to　analyze　the　rate　of　convergence　of　our　proposed　method,　we　characterize　the　Lipschitz　continuity　of　the　corresponding　solution　mapping　at　the　origin.　For　the　inner　problems,　we　show　that　the　positive　definiteness　of　the　generalized　Hessian　of　the　objective　function　in　these　inner　problems,　a　key　property　for　ensuring　the　efficiency　of　using　an　inexact　semismooth　Newton-CG　method　to　solve　the　inner　problems,　is　equivalent　to　the　constraint　nondegeneracy　of　the　corresponding　dual　problems.　Numerical　experiments　on　a　variety　of　large-scale　SDP　problems　with　the　matrix　dimension　n　up　to　4,　110　and　the　number　of　equality　constraints　m　up　to　2,　156,　544　show　that　the　proposed　method　is　very　efficient.　We　are　also　able　to　solve　the　SDP　problem　fap36　(with　n　=　4,　110　and　m　=　1,　154,　467)　in　the　Seventh　DIMACS　Implementation　Challenge　much　more　accurately　than　in　previous　attempts.