How the Arabic alphabet was organized has changed over the centuries. First was the abjad order going "a", "b", "j", "d" ; Then, someone decided to organize the alphabet by shapes so that letters made with the same shapes went right after each other (it is one prevalent alphabet organization and used everywhere). Then, recently, someone found a different way to organize it: by type of tail, then by type of shape, then by type of dot.
ه
ط ظ
ك م ي
ب ت ث ف
ج ح خ ع غ
ا د ذ ر ز و
س ش ص ض ق ل ن
1st Row: Looks different in all forms
2nd Row: Looks the same in all forms
3rd Row: Looks the same in the beginning form and middle form: ("odd-final" letters)
4th Row: Has the push-forward tail: ("push-forward tail" letters)
5th Row: Has the down-hook tail: ("down-hooked" letters)
6th Row: non-connectors: ("non-connectors")
7th Row (bottom row): has the bowl tail ("bowl-tailed" letters)