On my exam review sheet, the prof said that we would have a question where we would have to find 4 extensions of A by B (A,B groups of order 4 or less). My friend said that by research on possible extensions ( plus the fact that this is an introductory algebra course), he/she has concluded that it is most probable that A would have be Z_4, and B would have to be Z_2 (Do you have any input as to whether this is "most probable", considering this is an intro. course?). Now, I have two questions 1)Considering the groups mentioned above, I have come up with 4 extensions of A by B... (Z_4 X Z_2), Z_8, (The symmetries of a square), and Hamilton's Quaternions. What are other possibilities? I understand that I have asked about group extensions in another section, but I think this thread has somewhat of a difference. Thanks for the help.