The sequence of graphs starting with the Suzuki graph and successively taking local graphs, summarized in the following table, is known as the Suzuki tower, a name due to Jacques Tits (Leemans 2005).
More things to try:
Weisstein, Eric W. "Suzuki Tower." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SuzukiTower.html