赶紧, 连忙 and 赶快 (in addition to 马上, 立刻 and 立即) seem to mean 'immediately', 'forthwith'.
However, I don't really understand where their meanings overlap or if they are somehow different in a particular way. Does anyone know?
From what I can ascertain, it would seem that 连忙 is just a synonym of 马上,but 赶紧,赶快 are in a different category of sorts.