Which preposition to use with admittings

of Occurrences 12%

Families accustomed to such attendants have always about them humble dependents, whose children have no other prospect than domestic service to look forward to; to them it presents no degradation, but the reverse, to be so employed; they are initiated step by step into the mysteries of the household, with the prospect of rising in the service, if it is a house admitting of promotion,to the respectable position of butler or house-steward.

after Occurrences 1%

"A preposition may be known by its admitting after it a personal pronoun, in the objective case.

Which preposition to use with  admittings