I hope you find this helpful from from Kennedy’s latin primer:
The following rule with regard to the form of the Genitive Plural may be given for practical convenience:
Nouns with a syllable more in the Genitive Singular than in the Nominative Singular (Imparisyllabic Nouns) have Genitive Plural in -um.
Nouns with the same number of syllables in the Nominative Singular and Genitive Singular (Parisyllabic Nouns) have Genitive Plural in -ium.
The chief exceptions to this rule are the following:
(a) Imparisyllabic Nouns which have Genitive Plural in -ium are: glīs, līs, mās, mūs, nox, and Nouns of one syllable of which the Nominative Singular ends in -ns, -rs, -bs, -ps, -rx, -Ix; and neuters in -al, -ar.*****
Often also: fraus, rēn, lār, dōs, Nouns of two syllables with Nominative Singular ending in -ns, -rs, and most Nouns in -ās (gen. -ātis). These last and Nouns in -ns are especially variable. Horace writes both parentum and parentium, but the latter is rare.
(b) Parisyllabic Nouns which have Genitive Plural in -um are: canis, iuvenis, senex, sēdēs, pater, māter, frāter, accipiter.f
Sometimes also: apis, mēnsis, vatēs, volucris.
*****Nouns of one syllable, of which the Stem has two Consonants before i-, are only apparently Imparisyllabic because the Nom. Sing. originally ended in -is (46), and of some both forms are found; e.g. orbs and orbs. Similarly, neuters in -al, -ar originally ended -āle, āre (47).
fPater, mater, frâter, accipiter, are only apparently Parisyllabic because the e of the Nom. Sing, does not appear in the other cases.