What is the structure in the sentence no one could believe that she took dance classes at her age?

no one = (indefinite pronoun) subject of the sentencecould believe = auxiliary verb + main verb

that she took dance classes at her age = (relative clause) object of the sentence

that = (relative pronoun) introduces the relative clause

she = (personal pronoun) subject of the clause

took = verb of the clause

dance class = (compound noun) direct object of the clause

at = (preposition) introduces prepositional phrase 'at her age'

her = (possessive pronoun) describes object of the preposition 'age'

age = (noun) object of the preposition 'at'