bmf, the large gear is the clutch plate and should be held snug by the clutch spring when engaged. if it's wiggly, it's probably the main driveshaft bearings... if the clutch is NOT slipping horribly when trying to operate it.
There's bearings between that clutch plate with the gear, and the pucks in it, and the main driveshaft, but they would only show evidence of looseness when you dis-engaged the clutch by moving the lever.
Norm did a thread on clutches, and I did a few pics on how I took mine apart to grease those ball bearings. It's a little tricky, but do-able.
I did NOT pull my driveshaft because my bearings were good.
Biknut's recent teardown describes where you can takes off the chain sprocket, then drive the shaft out towards the clutch side of the engine... to replace those bearings.
Good luck
rc