The Semitic languages characteristically keep several s sounds apart and treat them as different consonants, and the inherited twenty-two letter alphabet gives each of them a sign. Mandaic keeps all three: as at fifteen, asz at eighteen, and ash at twenty-one, matching the places its relatives use.
Keeping them in writing and keeping them in speech are different things. The spoken language has blurred some of these distinctions, as it has blurred the gutturals, so the spelling of a classical Mandaic word preserves a contrast that a modern speaker may not make. That is the ordinary condition of a liturgical language, and the same gap between page and voice exists in Syriac.
The three letters are also spread widely through the alphabet rather than grouped, at the fifteenth, eighteenth and twenty-first places, which is a consequence of the inherited order and not of anything about the sounds. Nothing in the sequence collects related consonants together; the order is arbitrary and old, and that is exactly why it is such good evidence of descent when four alphabets share it.
Where a sound falls outside the inherited set entirely, Mandaic uses the affrication mark rather than a new letter. Marked ash covers the affricates that English writes ch and j, which loan words bring in constantly, so the sibilant letters carry more than their inherited share of the marked readings.