Wireless with Intel Centrino Advanced-N 6235
Since I'm now allowed to answer my question:
Okay, what I did to test this was:
sudo rmmod iwlwifi
sudo modprobe iwlwifi 11n_disable=1
So it seems like n-WLAN is the problem. To permanently make this work, I added options iwlwifi 11n_disable=1 to /etc/modprobe.d/iwlwifi.conf as first line after the comments.
This was confirmed by chili555's comment.