Fertility clinic costs 25.  Rush buy cost is build cost ^ 1.1 (truncated) * 6 for 204BC.

However, the minimum UPGRADE cost (i.e. overbuilding on an existing improvement) is 50 industrial units (with the exception of factoring in previous rush buys, but that is beyond the scope of your current question and in addition has been addressed elsewhere), which gives rise to the 438BC rush buy cost.

You'll also notice this with starports, as they only cost 20BC (156BC rush buy) on an empty tile but 438BC to (rush) overbuild.

Incidentally, this is the RUSH cost ONLY and does NOT affect how long it takes the improvement to build, if you build it normally.  It will simply take 25 industrial units (for the fertility clinic), 20 for the starport, etc, regardless of whether it's an empty tile or an overbuild.

As an additional note, although the game tells you in several places that you should only and/or get a bonus/discount/whatnot for upgrading over the same TYPE of improvement, there is in actuality NO CODE in the game that differentiates between improvement types, as far as upgrade COSTS are concerned.  (There is of course code that tells improvements what they're allowed to auto-upgrade to, but that's also not relevant to our discussion at present.)