How many characters are there on the icon of a Stack Exchange site?
CJam, 50 48 45 bytes

l22b391"þÁ "+{i%}/"Yª&gt;Þÿ9cîÂcVáòe~"322b4b=


There's unprintable characters in the strings above, which can be obtained by the snippets

[254 193 160]:c
[89 170 62 222 30 255 20 57 99 238 194 99 86 225 242 101 126 20]:c


This also shows that the code points are all below 256. Output is 0 for 1 letter, 1 for 2 letters, 2 for 3 letters and 3 for non-ASCII.

The program simply converts the input string to a base 22 number, performs a series of modulos to reduce the number down, before performing a lookup from a base-4 encoded table.

Try it online | Test suite