Mongia starred with bat and ball for the Foxes
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Leicestershire booked their semi-final place in the inaugural International 20:20 Club Championship and gained revenge on Somerset with a 66-run win.
The Foxes join Pakistan's Faisalabad Wolves, Chilaw Marians of Sri Lanka and the PCA Masters for Saturday's games.
Stung by Twenty20 Cup semi-final defeat to the Sabres, Darren Maddy (42), Dinesh Mongia (39) and John Sadler (40) helped Leicestershire to 172-8.
John Francis made 49 but Mongia's 2-6 in four overs sealed the victory.
Imran Khalid's Faisalabad Wolves made it through to Saturday
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Somerset had also lost the first match of the second day, with Faisalabad sealing a 30-run win after a tremendous all-round display from Mohammad Hafeez.
Hafeez hit 79 from only 35 balls to give the Wolves early momentum on their way to 207-5.
And he then took three wickets in Somerset's reply to bowl the Sabres out for 177, despite 82 from captain Ian Blackwell.
Chilaw beat South African Pro20 champions Nashua Titans by 67 runs, bowling them out for 112.
The Marians had set a target of 180 after Ishan Mutaliph (32) had got their innings off to a positive start and Nimesh Perara (39) carried on the momentum.