group_nameのみの集計を行ったものとjoinすれば良いと思います。
追記
group_nameのみの集計を行うサンプルです
Window関数
SQL
1select group_name, name
2 , avg(height)
3 , max(height)
4 , sum(case when height <= 170 then 1 else 0 end) as under170
5 , group_avg_height
6from (
7 SELECT U.group_name, U.name, A.height
8 , avg(height) over(partition by group_name) as group_avg_height
9 from countries as U
10 inner join players as A
11 on U.id = A.country_id
12) UA
13GROUP by group_name, group_avg_height, name
14ORDER by group_name, group_avg_height DESC
相関問合せ
SQL
1with UA as (
2 select U.id, U.group_name, U.name, A.height
3 from countries as U
4 inner join players as A
5 on U.id = A.country_id
6)
7select group_name, name
8 , avg(height),
9 , max(height),
10 , sum(case when height <= 170 then 1 else 0 end) as under170
11 , group_avg_height
12from (
13 SELECT *
14 , (select avg(height) from UA
15 where id=base.ID and group_name=base.group_name
16 ) as group_avg_height
17 FROM UA as base
18) UA
19GROUP by group_name, group_avg_height, name
20ORDER by group_name, group_avg_height DESC