I’m going to guess you named the system “fog” when you installed it?
CentOS 6.5 defaults the filesystem type to lvm disk management. The root partition is usually defaulted to a maximum size of 50 GB.
When FOG installs, it creates a directory in the root filesystem as /images which would be mounted on the root of the drive or / as you’re seeing.
If you need it to load to a different disk you can very simply. Just mv the /images to a folder on a filesystem that has much more space. My guess is /home in your case is also on it’s own filesystem labeled as:
/dev/mapper/vg_fog-lv-home.
