Step 1: Beneath the flexor tendons the palm is split by a septum into a radial pocket (thenar space) and an ulnar pocket (mid palmar space).
Step 2: Each digit drains pus into a specific pocket along its lumbrical canal. The index finger lies on the radial side and therefore links with the thenar space.
Step 3: The middle, ring and little fingers sit on the ulnar side and drain to the mid palmar space, which is the key contrast to remember.
Step 4: Since the question concerns the index finger, the infection travels to the thenar space. The hypothenar option is a distractor with no such communication.
\[\boxed{\text{Thenar space}}\]