my scenario : i tried the GetGroupByName method but didnt work,it cant find the group, i am not able to find the id of the group also.
GroupCollection groupColl = clientContext.Web.SiteGroups;
Group newgroup = clientContext.Web.SiteGroups.GetByName("InternalUsers");
clientContext.Load(groupColl);
clientContext.ExecuteQuery();
clientContext.Load(newgroup);
. Also ensure that you are passing the correct group name.