Podrías usar ntile :
SELECT car_id, "date",
ntile(CASE WHEN c <= 5 THEN 1
WHEN c <= 10 THEN 2
ELSE 3
END) OVER (PARTITION BY car_id ORDER BY "date") AS group_id
FROM (SELECT car_id, "date",COUNT(*) OVER(PARTITION BY car_id) AS c
FROM Table1) AS s
Salida:
╔════════╦══════════╦══════════╗
║ car_id ║ date ║ group_id ║
╠════════╬══════════╬══════════╣
║ 1 ║ 20160101 ║ 1 ║
║ 1 ║ 20160103 ║ 1 ║
║ 1 ║ 20160105 ║ 1 ║
║ 1 ║ 20160106 ║ 1 ║
║ 1 ║ 20160107 ║ 2 ║
║ 1 ║ 20160108 ║ 2 ║
║ 1 ║ 20160109 ║ 2 ║
║ 1 ║ 20160110 ║ 2 ║
║ 2 ║ 20160102 ║ 1 ║
║ 2 ║ 20160104 ║ 1 ║
╚════════╩══════════╩══════════╝
