SELECT searches.*, computers.name, sensorchecks.name AS Test FROM searches
LEFT JOIN computers
ON computers.computerid = searches.computerid
INNER JOIN sensorchecks
ON searches.searchid = sensorchecks.sensid
WHERE computers.name IS NOT NULL
ORDER BY NAME ASC
This SQL query will bring you back a list containing all the groups a computer is a member of, including the SearchID that is joining them to said group.