Fitting length of Dihedral groups

Question

Let $G$ be a dihedral group of order $2n$ where $n\geq 1$, denoted by $D_n$. We know that $G$ is nilpotent if and only if $n=2^i$ for all $i\geq 1$, a proof of this you can check in the below link 1. Thus, $G$ is nilpotent of fitting length 1 (refer to the link 2 for the definition of fitting length of a group). Now if $n\neq 2^i$ where $i\geq 1$, then the fitting length of $D_n$ is 2 since we have a fitting series $1\subset R \subset G$ where $1$ is the trivial subgroup and $R$ is the rotation group of $G$ and it is clearly of length 2. Is this correct? or there is any mistake?

[1] https://en.wikipedia.org/wiki/Fitting_length#:~:text=The%20Fitting%20length%20or%20nilpotent,Fitting%20chain%2C%20if%20one%20exists.

[2] Is the dihedral group $D_n$ nilpotent? solvable?