We know that Hagrid had his wand snapped after being accused of opening the Chamber of Secrets.
We know that Hadrid's wand segments were contained within a bright pink umbrella.
We can assume he was trying to hide his wand from the Ministry of Magic.
Surely if Hagrid was seen carrying a bright, pink, flowery umbrella, presumably with some sort of wooden pole or shaft - in all weather conditions, rain or shine - then anyone with half a brain would assume that it contained parts of a wand, or at the very least it would have some magic ability.
If Hagrid wanted to truly hide the fragments of his wand, surely something more inconspicuous would have been appropriate?