In the first book (here taken from the American version, Harry Potter and the Sorcerer's Stone), Ollivander describes Hagrid's wand.
"Rubeus! Rubeus Hagrid! How nice to see you again.... Oak, sixteen inches, rather bendy, wasn't it?"
"It was, sir, yes," said Hagrid.
"Good wand, that one. But I supposed they snapped it in half when you got expelled?" said Mr. Ollivander, suddenly stern.
"Er — yes, they did, yes," said Hagrid, shuffling his feet. "I've still got the pieces, though," he added brightly.
"But you don't use them?" said Mr. Ollivander sharply.
"Oh, no, sir," said Hagrid quickly. Harry noticed he gripped his pink umbrella very tightly as he spoke.
Hagrid's wand was not especially large. On the same page, Voldemort's wand is described as "thirteen-and-a-half inches" - Hagrid's wand was only two and a half inches longer. While most wands described in the books are less than a foot long, slightly longer wands are not wholly uncommon. On the higher end, the HP wiki states that the Elder Wand was fifteen inches long, and that the wand concealed in Lucius Malfoy's cane was eighteen inches long, but I can't confirm either of these pieces of information from canonical sources so far.
Hagrid's wand was certainly not large enough to be made into the staff of his umbrella - stick umbrellas are generally much longer than that, in the vicinity of three feet. (For instance, venerable British upper-class umbrella maker Swaine Adeney Brigg makes men's and women's wooden-shafted umbrellas in lengths from 33 to 38.5 inches.) Also, the wand is clearly not integrated into the umbrella in a visible way - Ollivander doesn't recognize it, and the only indication of anything unusual about the umbrella is the way Hagrid protectively clutches it when his wand is mentioned. The broken wand is most likely inside the shaft of the umbrella.
From this I think we can conclude that Hagrid had an ordinary wand. It was longer than most, but not umbrella-sized, and probably not outside the range of sizes that Ollivander and other wandmakers are accustomed to. It may have chosen Hagrid because he was well-suited to a long wand, but it was probably not custom-made for a person of his stature.