But the loss of the Volkswagen patriarch also raises the question of whether anyone, even the formidable Mr. Winterkorn, will bring the same resolve and attention to detail.

“Most people would say Piëch got the company going in a direction that made it one of the biggest car companies in the world,” Mr. Brauer said. “He has to be given credit for that.”

Volkswagen may also need to cut costs more aggressively, especially in Germany, a difficult task for a company that is 20 percent owned by the government of the state of Lower Saxony, and where labor unions exert strong influence.

Berthold Huber, former president of the IG Metall labor union and a member of the Volkswagen supervisory board, is serving as acting chairman of the company until a permanent successor to Mr. Piëch is named. That is the equivalent of the president of the United Automobile Workers overseeing Ford or General Motors.

Though Toyota produces more cars than Volkswagen, it has far fewer employees. Part of the discrepancy reflects the fact that Volkswagen produces more of its own components, like brake discs and seats, than Toyota, which buys more parts from outside suppliers. But the high number of employees is also a reflection of how hard it is to shrink the work force in Germany.

In Europe, Volkswagen is by far the biggest carmaker. All its brands together command a 23 percent market share in the European Union, more than double that of PSA Peugeot Citroën, the No. 2 automaker in Europe. But the European market, though recovering, does not offer the same long-term potential for growth as China, the United States and Latin America.

In much of the rest of the world, Volkswagen is struggling. In the United States, the second-biggest auto market after China, sales of all Volkswagen brands fell 2 percent last year, to about 600,000 cars, even as the overall market grew.