Minecraft wiki entry for Brewing, associated text: Although Jeb said that in Java Edition Beta 1.9 Prerelease 3 there would be 161 possible different potion combinations with 2,653 in the future, in the actual third pre-release only 22 different potions could be made without the use of external programs. Of those, 19 potions had one of 8 different effects.
By modifying the item NBT using an editor or commands, it is possible to get a potion that cannot be upgraded into a splash potion.
Unlike crafting, smelting and stonecutting, there is no in-game recipe book for brewing, making the process much less intuitive.