C# – Using Linq to group a list of objects into a new grouped list of list of objects

I don't know if this is possible in Linq but here goes…

I have an object:

public class User
{
  public int UserID { get; set; }
  public string UserName { get; set; }
  public int GroupID { get; set; }
}

I return a list that may look like the following:

List<User> userList = new List<User>();
userList.Add( new User { UserID = 1, UserName = "UserOne", GroupID = 1 } );
userList.Add( new User { UserID = 2, UserName = "UserTwo", GroupID = 1 } );
userList.Add( new User { UserID = 3, UserName = "UserThree", GroupID = 2 } );
userList.Add( new User { UserID = 4, UserName = "UserFour", GroupID = 1 } );
userList.Add( new User { UserID = 5, UserName = "UserFive", GroupID = 3 } );
userList.Add( new User { UserID = 6, UserName = "UserSix", GroupID = 3 } );

I want to be able to run a Linq query on the above list that groups all the users by GroupID. So the output will be a list of user lists that contains user (if that makes sense?). Something like:

GroupedUserList
    UserList
        UserID = 1, UserName = "UserOne", GroupID = 1
        UserID = 2, UserName = "UserTwo", GroupID = 1
        UserID = 4, UserName = "UserFour", GroupID = 1
    UserList
        UserID = 3, UserName = "UserThree", GroupID = 2
    UserList
        UserID = 5, UserName = "UserFive", GroupID = 3
        UserID = 6, UserName = "UserSix", GroupID = 3

I've tried using the groupby linq clause but this seems to return a list of keys and its not grouped by correctly:

var groupedCustomerList = userList.GroupBy( u => u.GroupID ).ToList();