With Republicans poised to seize control of the House and their odds of taking the Senate looking increasingly like a coin flip, internal divisions that have been sidelined by the need to stand united against the Democratic majority threaten to surface in a Republican-controlled Congress.

While headlines tend to focus on disarray among Democrats, the Republican Party is facing cleavages of a similar magnitude.

A political scientist at Middlebury College, Matt Dickinson, expects that the legislative productivity of a Republican House would largely depend on which party controls the Senate and the GOP leadership’s willingness to work with Democrats in the Senate or White House ahead of the 2024 election.

“In terms of bipartisan stuff there’s not a lot out there,” Mr. Dickinson said. “It in part comes down to the Republican leadership’s willingness to give Joe Biden something he can run on in 2024.”

He also says that Republicans are probably looking at the sort of House majority that will allow members of the right flank to leverage their voting power to extract concessions from both Democrats and their own party.

“The Republicans will have factions and they will have infighting just like the Democrats,” he says. “But there are enough issues that Republicans can coalesce around that they will pass some bills coming out of the House.”

Republicans are most likely to focus on raising the age for social security, extending President Trump’s tax cuts, and launching investigations, Mr. Dickinson said.

On other issues such as foreign policy and abortion, the party appears increasingly divided, even though disagreements about the party’s leadership — particularly the party’s relationship to Mr. Trump — are the most visible.

Last week, a former vice president, Mike Pence, spoke at the Heritage foundation on the future identity of the Republican Party, criticizing members who he called “apologists for Putin” and “unprincipled populists.”

Although Mr. Pence did not name anyone, Representatives such as Matt Gaetz and Paul Gosar or Republican candidates such the venture capitalist running for Senate in Ohio, J.D. Vance, have publicly criticized American support for Ukraine.

At the same event, Mr. Pence also drew attention to the party’s stance on abortion, a topic that has fallen in terms of electoral importance this election but is likely to dog the GOP in future elections.

Once united behind the idea of overturning Roe v. Wade, Republicans now face a party divided on how to follow through with instituting any new abortion policy.

Party leaders like the Republican National Committee chairwoman, Ronna McDaniel, have suggested that the GOP needs to meet voters where they are on the issue, which could mean instituting policies similar to Roe in many parts of the country.

Despite Ms. McDaniel’s advice, many Republican politicians and candidates have staked out positions in support of hardline bans on abortion — even in the case of rape or incest.

Highlighting the divisions in the GOP, various party elders have outlined different visions for the future of the party. Mr. Pence, Senator Scott, and the House minority leader, Kevin McCarthy, have all released competing platform proposals.

Mr. Pence this year released his “Freedom Agenda,” which focuses on “American culture” and prioritizes abortion and issues like allowing religious institutions to be politically active while maintaining their tax exemptions.

Mr. McCarthy’s “Commitment to America,” on the other hand, focuses on economic issues and crime.

Mr. Scott’s plan, “An 11 Point Plan to Rescue America,” leans on cultural and economic issues, suggesting that Republicans “eliminate all federal programs that can be done locally” and shrink the federal workforce by 25 percent.

Beyond dueling platforms, there are also looming divisions in the party’s coalition, primarily between more traditional establishment Republicans and the group that Mr. Pence called “unprincipled populists.”

The cleavage is perhaps best represented in the House by the prevalence of the Freedom Caucus, a group that has antagonized Republican leaders in the past.

In 2015, the recently founded group ousted the Speaker Boehner by opposing his leadership in the lower chamber. Speaker Ryan, who succeeded Mr. Boehner, also faced resistance from the caucus during his tenure.

In 2017, despite efforts by both Mr. Ryan and President Trump, the group thwarted the passage of the American Health Care Act, which would have repealed the Affordable Care Act.

In the event of a Republican majority, the leading contender for the position of speaker, Mr. McCarthy, will need to corral the Freedom Caucus, which opposed his leadership in 2015.

With forecasters like Sabato’s Crystal Ball predicting a relatively slim majority for Republicans, around 230 seats against 215 Democratic seats, the 42-member Freedom Caucus — or groups like it — will once again be able to command a great deal of power in the House.

One arena where the party’s right flank could exert its influence is in the election of a Republican speaker. A political scientist at John Jay College, Brian Arbour, says that even though Mr. McCarthy seems to have no clear rivals, Republicans have tossed speakers due to factional disputes in the past.

In an early sign of Mr. McCarthy’s intentions to court the group’s support, one of the most high-profile members of the Freedom Caucus, Representative Marjorie Taylor Greene, appeared next to the minority leader at the rollout of his “Commitment to America.”

Ms. Greene has said she will be “a strong legislator” and a “very involved member” of the next Congress. Unless Republicans win far more seats than they are expected to, she’s probably correct.

For these reasons, as well as the fact that any Republican majority in the House may be checked by a Democratic Senate, and certainly would be checked by a Democratic president, many expect the accomplishments of a Republican Congress to be relatively limited.

Mr. Arbour said any checks on Republican power are actually an advantage for party leadership trying to secure votes because “they don’t actually have to come to an agreement, they just have to oppose what the administration wants.”

Headlines about government funding and debt limit are likely to dominate news cycles in 2023, he said, in part because it is a way that a small number of representatives can win policy concessions.

“The biggest place where internal Republican divisions will show up will be in what to do about funding the government and the debt limit because these are the two things that have to be done,” Mr. Arbour said. 

On this point, Messrs. Arbour and Dickinson agree, with Mr. Dickinson predicting that “there’s going to be a lot of warfare and a lot of brinkmanship,” when it comes to funding the government.