Illustrator - object placements slightly off

I'm currently lerning Illustrator and I started building some Lego bricks for learning purposes. Building them worked, but when I try to stack them over each other, they just won't align proberly. Take a look at these screenshots:

This is how it looks when I drag and hold my grouped Lego object to where I want it. As you can see, the paths align perfectly.

But if I let go, that happens. The bricks aren't properly aligned, the blue brick is slightly shifted up and left.

Why does this happen? And how can I fix it? Thanks in advance!