For every group, there are 4! possible permutations (4 * 3 * 2 = 24) and there are four different groups so the number of different pickems at group stage is 244 or 331776.
After the group stage, there are 7 different matches with only 2 possible outcomes (Team A wins or Team B wins) so there are 27 or 128 different knockout combinations
Multiplying 331776 * 128 gives 42467328 different pickems
Fun fact: If we made a country where every habitant does a different pickem that country would have roughly the same population as Uganda