Agrupar por LIKE de un valor de columna

Puedes usar case :

SELECT (CASE WHEN plan_type LIKE 'silver%' THEN 'silver'
             WHEN plan_type LIKE 'gold%' THEN 'gold'
             WHEN plan_type LIKE 'platinum%' THEN 'platinum'
        END) as plan_grp, COUNT(*)
FROM subscriptions
GROUP by (CASE WHEN plan_type LIKE 'silver%' THEN 'silver'
               WHEN plan_type LIKE 'gold%' THEN 'gold'
               WHEN plan_type LIKE 'platinum%' THEN 'platinum'
          END);

Algunas bases de datos le permiten usar un alias de columna en el GROUP BY .