Hook: Floor Small (Green Square)The Cybernetic Supercomputer decoration fits into a small green square floor hook.
Hook: Floor Medium Narrow (Blue Rectangle)The Cybernetic Supercomputer decoration fits into a narrow blue medium rectangle floor hook.
Hook: Floor Medium (Blue Square)The Cybernetic Supercomputer decoration fits into a blue medium square floor hook.
How to Get a Cybernetic Supercomputer Decoration
Every time you complete your personal conquest, you receive a lockbox with three random conquest Crafting Node Decorations, one of which could possibly be a Cybernetic Supercomputer. You get a second lockbox if you complete your guild conquest goal as well.
If you're looking to get a Cybernetic Supercomputer and haven't gotten lucky with your conquest rewards, you can buy one from the GTN from another player. These decorations are farily inexpensive because there is an unlimited supply - more are created every time someone finishes their conquest goal.