Champions Kent will travel to Edgbaston to play Warwickshire in the Twenty20 Cup quarter-finals after beating Sussex in their final group match on Friday.
Yorkshire also had to win their last match - at Trent Bridge - to make the last eight and will travel to Durham.
Essex host Northants after knocking out Hampshire while Middlesex will play Lancashire at The Oval because Lord's is staging a Test on 10 July.
The matches will take place on 7, 8 and 9 July, with the finals on 26 July.
Warwickshire, who were unbeaten until Friday, are sure to give Kent a stern test at their Edgbaston headquarters.
But bookmakers installed Durham - the only other team to lose just one match - as their favourites for the competition.
Durham v Yorkshire
Essex v Northamptonshire
Middlesex v Lancashire
Warwickshire v Kent