1923 is quite similar to what we are seeing right now.
The GOP in general held a slight majority, with party itself fractured between mainstream GOP, Progressive GOP, and an Independent branch of the GOP.
Overall split of the GOP-dim split going into the 68th Congress was 209-195. As then there were 414 in the House. So Gillett needed 208 votes to secure Speaker's role.
Party Leader Frederick Gillett of NH fell short 12-15 votes short for the 1st 8 ballots, before he forged and alliance on the 9th ballot with the progressive branch with the party.
Does the Freedom Caucus hold firm, or take the same approach after some negotiations?
https://www.ourcampaigns.com/RaceDetail.html?RaceID=56312