It's curious that Cessna skipped the "I" model designation for the 182, even though there was a 172I.
Looking for consistency in Cessna's model number protocol will drive you nuts.
A retractable 172 is a Model 172RG. A retractable Cardinal is a Model 177RG. So of course a retractable 182 is a ... nope, it's a Model R182. But a Model R172 is a fixed-gear 172 with a bigger engine. And don't confuse the Model R182 with the Model 182R (or an R172 with a 172R). Or the Model 182T, or a turbocharged Model T182. You could also have a fixed gear Model T182R, but the turbo'ed retractable is the Model TR182. Still with me?
A Model P172 was a 172 with more horsepower, but a Model P206 had the same engine as the other 206's but with nicer seats and no cargo door. And a Model P210 was a 210 with pressurization.
Put an 'A' in front of a Model 150 or 152 (A150/A152) and you've made it aerobatic. Put an 'A' in front of a 185 Skywagon or 188 Agwagon and you've made it with a bigger engine. Put an 'A' in front of a 182 and you've made it ... in Argentina!
But the 172I was probably an afterthought, reflecting a last-minute change in the company's plan.
Recall that the 172H was supposed to be the last of the old-fashioned, strutted 172s. Cessna was developing a snazzy, modern, strutless replacement that originally was to be called the Model 172J. Former Cessna aerodynamicist and test pilot Bill Thompson picks up the story:
"As early as 1965 we had envisioned a C-172 replacement in the form of the totally new cantilever-wing C-177. In anticipation of a great sales success, our management had taken a leap of faith by ordering 4,000 Lycoming O-320-E2D 150hp engines for that airplane. When this "bigger and better" airplane turned out to be too heavy, it became clear that 150 hp was inadequate for the C-177. Thus it was necessary to use some of these 4,000 engines in a continued C-172I production program. The charmed life of the C-172 was destined to continue indefinitely with this smoother-running and lighter 4-cylinder Lycoming engine."
Since the 1967 model was 172H, and 172J was already taken for the Cardinal project, "172I" was available for the stop-gap Lycoming-powered 172 for 1968. Only 649 172Is were built, compared to 1,620 for the 1967 172H, and 1325 for the 1969 172K.