Three weeks after former President Donald J. Trump was indicted on charges of illegally retaining national security records and obstructing the government’s efforts to reclaim them, a federal grand jury in Miami is still investigating aspects of the case, according to people familiar with the matter.

In recent days, the grand jury has issued subpoenas to a handful of people who are connected to the inquiry, those familiar with it said. While it remains unclear who received the subpoenas and the kind of information prosecutors were seeking to obtain, it is clear that the grand jury has stayed active and that investigators are digging even after a 38-count indictment was issued this month against Mr. Trump and a co-defendant, Walt Nauta, one of his personal aides.

Prosecutors often continue investigating strands of a criminal case after charges have been brought, and sometimes their efforts go nowhere. But post-indictment investigations can result in additional charges against people who have already been accused of crimes in the case. The investigations can also be used to bring charges against new defendants.

When the office of the special counsel Jack Smith filed the charges against Mr. Trump and Mr. Nauta in the Southern District of Florida, the 49-page indictment offered an unusually detailed picture of the former president holding on to 31 highly sensitive government documents at Mar-a-Lago, his private club and residence in West Palm Beach, Fla. Among the documents were some that concerned U.S. nuclear programs and others that detailed the nation’s potential vulnerabilities to attack.

The indictment was strewn with vivid photographs of government records stored in boxes throughout Mar-a-Lago in a haphazard manner. Some of the boxes were piled up in a storage room, others in a bathroom and on a ballroom stage.

Several of Mr. Trump’s aides and advisers appeared in the indictment, identified only as Trump Employee 1 or similar descriptions. In one episode, the indictment recounted how Mr. Trump displayed a classified map to someone described as “a representative of his political action committee” during a meeting in August or September 2021 at his golf club in Bedminster, N.J.

The representative of the PAC was Susie Wiles, one of the top advisers for Mr. Trump’s presidential campaign, according to two people briefed on the matter. A Trump spokesman declined to comment.

Ms. Wiles’s appearance in the indictment was reported earlier by ABC News.

The fact that Ms. Wiles could become a prosecution witness should Mr. Trump’s case go to trial, even as she is helping run his third bid for office, underscores the complexities that the former president now faces as he deals with both a presidential campaign and a criminal defense with an overlapping cast of characters.

During the meeting with Ms. Wiles, the indictment says, Mr. Trump commented that “an ongoing military operation” in an unnamed country was not going well. He then showed Ms. Wiles, who did not have proper security clearance, a classified map of that country, the indictment says, even while acknowledging that he should not be displaying the map and warning Ms. Wiles “to not get too close.”

Many of Mr. Trump’s aides and employees at Mar-a-Lago were questioned as part of the investigation that resulted in his indictment, and Mr. Trump has been barred from discussing the facts of the case with them even though many work in close contact with him. Mr. Trump has made defending himself against the charges a central part of his political and fund-raising messages, adding to the level of overlap that exists between his legal and political worlds.

Other aides who have been close to Mr. Trump are featured in the indictment, such as “Trump Employee 2,” who has been identified as Molly Michael, an assistant to Mr. Trump in the White House and his post-presidential office. The portion of the indictment describing the transcript of an audio recording in which Mr. Trump described what he said was a plan to attack Iran given to him by the Pentagon lists someone as a “staffer,” whom three people identified as Liz Harrington, a spokeswoman for Mr. Trump.

Some Trump aides and employees who had initially caught the attention of investigators were mentioned in the indictment only in passing.

At one point, for example, prosecutors under Mr. Smith appeared to be focused on Mr. Nauta’s dealings with a maintenance worker at Mar-a-Lago, Carlos Deoliveira, who helped him move boxes into a storage room at the compound. The movement of those boxes — at Mr. Trump’s request, prosecutors say — ultimately lay at the heart of a conspiracy charge in the indictment accusing Mr. Trump and Mr. Nauta of obstructing the government’s attempt to retrieve all of the classified materials in Mr. Trump’s possession.

In a previously unreported detail, prosecutors obtained a warrant to seize Mr. Deoliveira’s phone as part of their investigation, according to a person familiar with the matter.

Records from the phone eventually showed that Mr. Deoliveira called an I.T. specialist who worked for Mar-a-Lago last summer around the time that prosecutors issued a subpoena to Mr. Trump’s company, the Trump Organization, demanding footage from a surveillance camera near the storage room where the boxes of documents were kept.

But Mr. Deoliveira is referenced as “an employee of the Mar-a-Lago Club” in only a single paragraph in the indictment.

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