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brògshoefeminine noun
the
a' bhròg
after a preposition
a' bhròg
of the
na bròige
plural
brògan
the (plural)
na brògan

Every form but the headword, the genitive and the plural is worked out by the spelling rules in the grammar guide, so what you see here is what the guide teaches. Awaiting a fluent speaker’s review.