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We statistically study the relationship between the Lyman-alpha (\lya) and 1--8 Å soft X-ray (SXR) emissions from 658 M- and X-class solar flares observed by the {\em Geostationary Operational Environmental Satellite} during 2006--2016. Based on the peak times of the two waveband emissions, we divide the flares into three types. Type I (III) has an earlier (a later) peak time in the \lya\ emission than that in the SXR emission, while type II has nearly a same peak time (within the time resolution of 10 s) between the \lya\ and SXR emissions. In these 658 flares, we find that there are 505 (76.8\%) type I flares, 10 (1.5\%) type II flares, and 143 (21.7\%) type III flares, and that the three types appear to have no dependence on the flare duration, flare location, or solar cycle. Besides the main peak, the \lya\ emission of the three type flares also shows sub-peaks which can appear in the impulsive or gradual phase of the flare. It is found that the main-peak (for type I) and sub-peak (for type III) emissions of \lya\ that appear in the impulsive phase follow the Neupert effect in general. This indicates that such \lya\ emissions are related to the nonthermal electron beam heating. While the main-peak (for type III) and sub-peak (for type I) emissions of \lya\ that appear in the gradual phase are supposed to be primarily contributed by the thermal plasma that cools down.