Vertex count increases drastically when exporting to .FBX I am trying to export FBX file from Blender so I could use it in my OpenGL app, but when I export it, the vertex count increases from ~6k to ~25k. 

I wouldn't really mind it, but I additionally have a text file with segmentation where vertex groups are assigned to body parts, 
e.g. "right_hand: 0, 1, 2, ... , 193; left_hand: 194, 195, ... , 435; ..."

So, when I load the model(with Assimp btw) in my app and try to render segmentation, almost all the vertices are wrong.

Do you guys have any thoughts about it?

Oh and one last thing, when I import the model back to Blender, the vertex count becomes ~6k again and everything works fine(textures,normals, e.t.c) just like before.
I would generally blame the fact that many programs hate quads (not without reason; graphics cards usually only use tris, so it splits them into tris, regardless). However, that shouldn't change your vertex count so drastically since it's only changing face count, and should retain the same number of vertices. It seems likely, then, that you have some sort of modifier in place, subsurf is the usual suspect, that hasn't been applied. Try applying all your modifiers before exporting, and see if this solves your issue.