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Calculating quotient groups and normal subgroups

Posted 5 months ago
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Hello! I am trying to calculate all the quotient groups of the D4 group. I'm using the following Mathematica function to do so:

Q = FiniteGroupData[Group, "QuotientGroups"]

Which produces

{"Trivial", {"CyclicGroup", 2}, {"DihedralGroup", 
  2}, {"DihedralGroup", 4}}

I found the Normal subgroups as well, by doing

r = FiniteGroupData[Group, "NormalSubgroups"];
r = DeleteDuplicates[r, 
  IsomorphicGraphQ[FiniteGroupData[#1, "CycleGraph"], 
    FiniteGroupData[#2, "CycleGraph"]] &]

and got

{{"CyclicGroup", 1}, {"CyclicGroup", 2}, {"CyclicGroup", 
  4}, {"DihedralGroup", 2}, {"DihedralGroup", 4}}

According to the documentation centre the possible quotient groups, are obtained by finding the quotient with respect to normal subgroups, my question is if there's a way of knowing which normal subgroup was used to get each quotient group. For example, is there a way to know that the normal subgroup used to get the quotient group D2 was C2? I haven't found any way of doing this and could use some help, please.

Thanks!

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