Groups of order 12

It is one of my favorite exercises at the end of the term when students are stuffed with all those notions of generators and factor groups and p-groups and lower/upper central series and different decompositions of Jordan-Hölder and outer automorphisms and so on.

I just say -- I believe that here you have all graphs of subgroups for groups of order 12:

Z12

Z2xZ6

A4

Q3

D6

Click on any to see the graph, or see all.

But why should you believe me? Please, confirm whether there are other groups of that order; find out the meaning of all the symbols used there and verify that one actually has full graphs of the subgroups; invent alternative methods to represent them (for example, how to avoid replication of conjugate subgroups?); apply all your theoretical tools to these small, simple examples.

And when they work on it I have time for a cup of coffee. In fact, a very long series of cups of coffee.

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        the same, in Polish