That's a good start.
Tarot
|- Trifoni
|- Oracle
Does that seem reasonable?
The word is actually spelled "Trionfi" It's the oldest name for Tarot cards. It's an Italian word with a double meaning of "triumphs" or "trumps". The original theme of Tarot is one of triumphal processions and the English word "trump" is derived from this word.
http://en.wikipedia.org/wiki/Trionfi_(cards)
However this word is not well known except mostly by Tarot historians. Instead of "Trionfi" I would use "Tarot Games" or "Tarot Playing Cards" which could be a traditional type of trick taking or fantasy/RPG sort.
I think oracles should be a separate category like playing cards is a separate category. Oracle is not a subset of Tarot. It is more of a superset where Tarots designed for divination would be a subset of oracle. In lieu of the word "oracle" in the Tarot category, I would have "Tarot reading/divination" or something to that effect.
Tarot
|- Tarot games
|- Tarot divination
Oracles
|- Lenormand
|- other
Playing cards
|- Standard 52 card decks
|- variant playing cards
You may notice I've not used the word "cards" when discussing divination. One thing to keep in mind is that dice are also used in divination and TGC allows one to create custom 6 sided dice. A divination category should allow for the creation of such dice in addition to cards.