The heavier the aircraft, the more wheels it'll require to hold up the mass on the ground (and the impact force on landing). That said the empty weight and max takeoff weight of the the C-17 (~130tons empty, ~265tons max) is greater than the Il-76 (~100tons empty, ~200tons max), so I'd hypothesize that the C-17's wheels are probably made of material that allows it to supporting more mass per wheel than the Il-76, thereby also freeing up valuable space and weight for the plane to carry additional load.The C-17, Il-76, and Y-20 are close equivalents. However, there are notable differences in landing gear design among them.
The C-17 landing gear configuration is 1 frontal (2 wheels), 4 rear (grouped in 3); 14 wheels total.
The Il-76 landing gear configuration is 1 frontal (4 wheels), 4 rear (grouped in 4); 20 wheels total.
The Y-20 landing gear configuration is 1 frontal (2 wheels), 6 rear, (grouped in 2); 14 wheels total.
What are the advantages and disadvantages of each arrangement and why does the Il-76 have so many wheels on its landing gears? Does this have to do with Russia's landing gear technology being behind that of US and China?