2

I'm trying to center the fifth row and make the $\{...\}$ closer together, unfortunately I don't know much latex.

\psset{nodesep=2pt}
\newpsstyle{DblDash}{linestyle=dashed, dash=1pt 1.5pt, doubleline}
\begin{psmatrix}[mnode=r,colsep=0.3,rowsep=0.5]

 & &[name=1] $D_6$ \\

 & [name=2] $\{e,a,a^2,a^3,a^4,a^5\}$ & [name=3]$\{e,a^2,a^4,b,a^2b,a^4b\}$ &                                         [name=4]$\{e,a,a^2,a^4,ab,a^3b,a^5\}$ \\

 &[name=5] $\{e,a^3b,b,a^3b\}$ &  [name=6] $\{e,a^3,a^2b,a^5b\}$ &  [name=7] $\            {e,a^3,ab,a^4b\}$ \\

& & [name=8] $\{e,a^2,a^4\}$ \\

&[name=9]$\{e,b\}$ &[name=10]$\{e,ab\}$ & [name=11]$\{e,a^2b\}$ &[name=12]$\{e,a^3b\}$ & [name=12]$\{e,a^4b\}$ & $\{e,a^5b\}$ & [name=13]$\{e,a^3\}$ \\
&& [name=14]$\{e\}$

\ncline{1}{2}\ncline{1}{3}\ncline{1}{4}
\ncline{2}{5}\ncline{2}{6}
\ncline{3}{6}\ncline{4}{7}\ncline{4}{6}
\ncline{5}{8}\ncline{6}{8}\ncline{7}{8}
\ncline{9}{14}\ncline{10}{14}\ncline{11}{14}
\ncline{12}{14}\ncline{13}{14}\ncline{8}{10}
\ncline{8}{9}\ncline{8}{11}\ncline{8}{12}\ncline{8}{13}
\end{psmatrix}

enter image description here

2

Does this code give what you want?

 \documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}%
\usepackage{lmodern}
\usepackage[nomarginpar, textwidth = 16cm]{geometry}
\usepackage[svgnames,x11names]{pstricks}%%, pdf
\usepackage{pstricks-add}
\usepackage{multido}
\usepackage{mathtools}

\pagestyle{empty}
\begin{document}

\psset{nodesep=3pt}
\newpsstyle{DblDash}{linestyle=dashed, dash=1pt 1.5pt, doubleline}
 \begin{psmatrix}[mnode=r,colsep=0.5,rowsep=0.75]
%
  &  & &[name=1] $ D_6 $ &\\
%
   & [name=2] \clap{$ \{e,a,a^2,a^3,a^4,a^5\} $} & & [name=3]\clap{$ \{e,a^2,a^4,b,a^2b,a^4b\} $} &   &                                        [name=4]\clap{$ \{e,a,a^2,a^4,ab,a^3b,a^5\} $}& \\
%
&[name=5] $ \{e,a^3b,b,a^3b\} $ & &  [name=6] $ \{e,a^3,a^2b,a^5b\} $ & &   [name=7] $ \{e,a^3,ab,a^4b\} $ \\
%
& & & [name=8] $ \{e,a^2,a^4\} $ & &\\[6pt]
%
[name=9]\quad$ \{e,b\} $\quad&[name=10]$ \{e,ab\} $ & [name=11]$ \{e,a^2b\} $ &[name=12]$ \{e,a^3b\} $ & [name=13]$ \{e,a^4b\} $ & [name=14]$ \{e,a^5b\} $ &[name=15]\enspace $ \{e,a^3\} $\quad &\\[6pt]
 & && [name=16]$ \{e\} $
%
\ncline [offsetB=-7pt]{1}{2}\ncline{1}{3}\ncline[offsetB=7pt]{1}{4}
\ncline{2}{5}\ncline[offsetA =-6pt ,offsetB=-6pt, nodesepB =4pt]{2}{6}%offsetB=3pt,
\ncline{3}{6}\ncline{4}{7}\ncline[offsetA=6pt, ,offsetB=6pt, nodesepB = 4pt]{4}{6}
\ncline[offsetA =-8pt, nodesepA = -4pt ,offsetB=-5pt]{5}{8}\ncline{6}{8}\ncline[offsetA =8pt, nodesepA=-4pt ,offsetB=5pt]{7}{8}%
\ncline{8}{9}\ncline{8}{10}\ncline{8}{11} \ncline{8}{12} \ncline{8}{13} \ncline{8}{14} \ncline{8}{15}
\ncline{9}{16}\ncline{10}{16}\ncline{11}{16} \ncline{12}{16} \ncline{13}{16} \ncline{14}{16} \ncline{15}{16}
\end{psmatrix}

\end{document} 

enter image description here

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