NEW YORK >> Three Yorkshire terriers nestle in a man’s arms on a train. A pug lounges on a bench. A chow chow on a leash mingles among commuters.

For regular riders of the New York City subway, chances are you are seeing more dogs these days, and they are often riding out in the open (or close to it), right alongside their owners.

Once rare, such sightings elicit coos and smiles from plenty of pet-friendly riders, but perhaps just as many steely glares from passengers who are perturbed by the intrusions.

The scofflaw dogs appear here and there on platforms and trains in plain sight, defying the rule that they must be in closed carriers of some sort and surfacing often enough on social media the instant the train is back in cell range.

When Hannah O’Keefe, 24, spotted the chow chow on an A train in Manhattan the day before Thanksgiving, she snapped a photo and posted it on Twitter to express gratitude for the chance encounter.

“If it’s a cute dog, I’m like, ‘I know you’re not supposed to be here, but I’m happy you’re here,’” said O’Keefe, who lives in Brooklyn and works at a nonprofit.

Unmistakable as the increase may be to daily riders, it is impossible to quantify how many dogs are riding the rails. Many pet-toting riders might never cross paths with a police officer. Or an officer, instead of issuing a summons, might ask the owner — and the dog — to leave the system.

Only 219 riders were issued summonses last year for having unauthorized animals on subways and buses, down from 261 in 2014, according to the police.

To put those totals in perspective, more than 75,000 summonses were issued across the transit system in 2015, for matters such as fare evasion and seat obstruction.

Police dogs are not an unusual sight in the transit system, nor are service dogs, aiding people who are blind or otherwise disabled. But such animals are highly trained and generally accustomed to the underground environment.

The seemingly scant enforcement does not mean that dogs do not occasionally create headaches for subway officials. In November, a Rottweiler puppy escaped its leash and had to be rescued from the tracks by a subway worker. Last February, a dog had to be similarly extracted after ending up on the tracks near the Fordham Road station.

They are not the only pets to get into trouble. Two kittens wound up on the tracks in 2013, snarling service and inserting themselves into the New York City mayoral race when Joseph J. Lhota, a Republican candidate who was previously chairman of the Metropolitan Transportation Authority, said trains should have kept running (Lhota lost to his Democratic opponent, Bill de Blasio). Another cat, this one named George, got onto the tracks at the Canal Street station in July, delaying dozens of trains.

While most dogs prompt nothing more pointed than a stare from riders, they occasionally draw more aggressive displays of displeasure. In December, a man was arrested after he punched a pit bull therapy dog as well as the man who had brought the animal onto the No. 4 train. The assailant had asked the man to move the dog away from him, the police said.

The day-to-day commotion underground could seem overwhelming for dogs, but some appear to enjoy the adventure. Marnie the Dog, a celebrity Shih Tzu with nearly 2 million followers on Instagram, recently pranced through the subway on a leashless joy ride chronicled in a video posted online.

Many riders claim to be unaware of the rules. Unlike signs that remind riders that smoking and moving between train cars are not allowed, the restrictions on dogs are not widely posted. On a No. 7 train from Manhattan to his home in Queens, Amaru Alzogaray, a dog walker, was transporting three Yorkshire terriers for which he regularly cares. A taxi ride could cost $60, he said.

“I didn’t know that you had to have them inside a bag,” Alzogaray said. “I thought only that they have to be well-behaved and not dangerous to other people.”

To some, bringing a dog onto the subway is not unlike nail-clipping or so-called manspreading. They say it should be similarly scorned by subway officials and included in the current campaign for improved subway etiquette.

Mariel Conway, 28, was miffed last year when she saw a dog taking up two subway seats while an older rider was left standing nearby.

“This guy was just letting the dog spread out, which during rush hour was really annoying,” said Conway, who works in the entertainment industry.

Riders with unauthorized animals can face a $25 fine, lower than the penalty for smoking ($50) or fare evasion ($100). If a dog poses a “direct threat” to other passengers, the animal and the owner can be ejected from the system.

Chris Cerritelli, 25, knows he is breaking the rules. On jaunts to Central Park and the Brooklyn waterfront with his boxer Mister, friendly riders say hello and ask to pet the dog. He has been stopped by an officer just once, he said, and he thinks the police are right to focus on other matters.

“It shouldn’t be their priority — they have a hundred thousand other things to worry about,” said Cerritelli, a furniture designer.

Chief Joseph Fox, the head of the Transit Bureau at the Police Department, said officers used common sense to decide whether to issue a violation or ask someone to leave a train.

As for what counts as a carrier, officers are not given a precise definition, Fox said. “If it’s something that prevents the dog from alarming somebody or sticking their head out and taking a snap at somebody, I think they would probably consider that a carrier,” Fox said.

Over the summer, Fox saw firsthand a bit of the enforcement. He was riding the subway on his day off with his daughter and a service dog she was training. An officer approached his daughter and said she could not bring the dog into the station. But she explained that he was a service animal, and after showing the officer the dog’s special jacket, he said they could proceed. At the end of the encounter, the officer recognized the chief and apologized, but Fox said he thanked the officer for doing his job.

While service dogs are allowed on leashes, therapy and emotional support animals are not permitted outside carriers. But as the number of people with such animals grows — increasingly inspiring controversy on airplanes, college campuses and in residential buildings — some officers might not know the difference.

Marie Leger came across an unusual sight on the subway last year: a dog riding on a seat near a cat that was wandering the aisle, both with the same family. Riders did not bat an eye as the cat rubbed up against passengers’ legs.

Leger, 42, a dermatologist, said she often saw dogs riding the subway outside carriers.

“I usually find it charming,” she said. “But if the whole subway was full of misbehaving animals, I probably wouldn’t be so delighted.”