Get the Term Group from current site using Server Side object model

Group group= null;

_siteId = SPContext.Current.Site.ID;

using (SPSite site = new SPSite(_siteId))
   {
       TaxonomySession taxonomySession = new TaxonomySession((SPSite)site);
        if (taxonomySession.TermStores.Count != 0)
           {
               TermStore termStore = taxonomySession.TermStores[0]; //default term store
                group = termStore.Groups["group name"];

           }
   }