Groups of order 18

There are 5 groups of order 18:

gap> grp(18);
Group 1 has structure: D18 and is Non-Abelian
Group 2 has structure: C18 and is Abelian
Group 3 has structure: C3 x S3 and is Non-Abelian
Group 4 has structure: (C3 x C3) : C2 and is Non-Abelian
Group 5 has structure: C6 x C3 and is Abelian

The workhorse here is the function ConstructAllGroups and is part of the GAP package GrpConst.

#
# Prints all groups of order n
# IN: Group
#
grp:=function(n) 
local listGroups;
listGroups:=ConstructAllGroups(n);
i:=1;
while(i<(Length(listGroups)+1)) do
 Print("Group ");
 Print(i);
 Print(" has structure: ");
 Print(StructureDescription(listGroups[i]));
 Print(" and is ");
 if (IsAbelian(listGroups[i])) then
  Print("Abelian");
 else
  Print("Non-Abelian");
 fi;
 Print("\n");
 i:=i+1;
od;
end;

Permutations

Whatever you have to do with a structure-endowed entity S try to determine its group of automorphisms . . . You can expect to gain a deep insight into the constitution of S in this way.
Herman Weyl, Symmetry ( Quote found in this PDF )

Is it possible to translate the above sentence to "Jip en Janneke"-language? Before anything else I should give it a try myself.