I saw this question earlier on the forum and was wondering if my result to it was correct!
If D14 is the dihedral group acting on a heptagon, are the only subgroups in the lattice D14, < r> , < o> and e? Where o is rotation and r is reflection and < x> gives the group generated by x.
My thought process was that < o^n> would not be unique as it would generate exactly the some thing as < o> and everything else would generate the entire group so not be a subgroup. Is my thinking correct?
Am I also right in thinking the centre is just (e) and the normal subgroups are just D14, (e) and < o>.