The land of the sticks

In the land of the sticks, there was once a great committee of 52 stickmen. The committee was made out of wise sticks from all over the land and sea, and it governed the laws of the land of the sticks.

The committee was divided into 4 subcommittees, S, H, C, and S', each comprising of 13 members, officially known as A,2,3,4,5,6,7,8,9,10,J,Q,K.

At the head of the committee, was a tall and long stick, called Chopstick. He was the pinnacle of the committee (due to h8), and he stood tall, towering above the committee on the podium one day, and with a booming voice he nearly roared, "Today, we have a chemical bonding exercise. The purpose of this exercise is to improve the chemistry of members of the committee, as well as to make sure the members of the committee are strongly bonded."

"In this exercise, you will first do 20 pushups (O,N,E,1,T,W,O,2,...) and 5 chinups, and then get into your assigned groups."

The truth is, Chopstick had not assigned the groups.

To make matters worse, each person in Stickland hates exactly 3 people in the committee, and it would be counterproductive to put 2 sticks who hate each other in the same group.

Chopstick wants to minimise the number of groups, as the efficiency of his program to analyse the data of each group runs in O(n!) time.

Given that Chopstick is a very unlucky stick (Worst case scenario), state the minimum number of groups possible.