@flamber, actually, Metabase does not generate HAVING to filter on aggregated data, instead it wraps the initial query in a subquery, and filters it with an outer WHERE.
One of the unfortunate outcomes is that such Question's fields cannot be assigned to Dashboard filters, as we discovered here. This is super sad.
Example query generated with Question builder:
SELECT source.InitiatorGroup AS InitiatorGroup, source.count AS count
FROM (SELECT v_servicedesk.InitiatorGroup AS InitiatorGroup, count(*) AS count FROM v_servicedesk
WHERE date(v_servicedesk.GroupModifiedOn) BETWEEN date(date_add(now(), INTERVAL -30 day))
AND date(now())
GROUP BY v_servicedesk.InitiatorGroup
ORDER BY v_servicedesk.InitiatorGroup ASC) source WHERE source.count > ?
LIMIT 1048576
