\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}

\usetikzlibrary{arrows}
\usetikzlibrary{intersections}
\usetikzlibrary{math}
\usetikzlibrary{positioning}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{shapes.misc}
\usetikzlibrary{calc}

\begin{document}
\begin{tikzpicture}[
    >=latex, 
    classcirc/.style = {
      draw = gray, thick, circle,
      minimum size = 12mm,
      inner sep = 0pt, outer sep = 0pt,
    },
    classlabel/.style = {
      below right = 5mm
    },
    round/.style = {
      draw = orange, thick, circle,
      minimum size = 1mm,
      inner sep = 0pt, outer sep = 0pt,
    },
    cross/.style = {
      cross out, draw = magenta, thick,
      minimum size = 1mm, 
      inner sep = 0pt, outer sep = 0pt
    },
  ]
  \matrix [row sep = 3mm, column sep = 0mm] {
    \node[classcirc] (C1)  {} node[classlabel] {\(C_{1}\)};  & 
    \node[classcirc] (C2)  {} node[classlabel] {\(C_{2}\)};  &
    \node[classcirc] (C3)  {} node[classlabel] {\(C_{3}\)};  &
    \node[classcirc] (Ci)  {} node[classlabel] {\(C_{i}\)};  &

    \node[classcirc] (Cs)  {} node[classlabel] {\(C_{s}\)};  &
    \node[classcirc] (C3i) {} node[classlabel] {\(C_{3i}\)}; &
    \node[classcirc] (C2h) {} node[classlabel] {\(C_{2h}\)}; &
    \node[classcirc] (D2)  {} node[classlabel] {\(D_{2}\)};  \\

    \node[classcirc] (D3d) {} node[classlabel] {\(C_{3v}\)}; &
    \node[classcirc] (C2v) {} node[classlabel] {\(C_{2v}\)}; & 
    \node[classcirc] (D2h) {} node[classlabel] {\(D_{2h}\)}; & 
    \node[classcirc] (D3)  {} node[classlabel] {\(D_{3}\)};  &

    \node[classcirc] (C4)  {} node[classlabel] {\(C_{4}\)};  &
    \node[classcirc] (C6)  {} node[classlabel] {\(C_{6}\)};  &
    \node[classcirc] (D3dP) {} node[classlabel] {\(D_{3d}\)}; &
    \node[classcirc] (S4)  {} node[classlabel] {\(S_{4}\)};  \\

    \node[classcirc] (S3)  {} node[classlabel] {\(S_{3}\)};  &
    \node[classcirc, dashed] (T)   {} node[classlabel] {\(T_{}\)};   &
    \node[classcirc] (C4h) {} node[classlabel] {\(C_{4h}\)}; &
    \node[classcirc] (C6h) {} node[classlabel] {\(C_{6h}\)}; &

    \node[classcirc, dashed] (Th)  {} node[classlabel] {\(T_{h}\)};  &
    \node[classcirc] (C4v) {} node[classlabel] {\(C_{4v}\)}; &
    \node[classcirc] (C6v) {} node[classlabel] {\(C_{6v}\)}; &
    \node[classcirc, dashed] (Td)  {} node[classlabel] {\(T_{d}\)};  \\
    
    \node[classcirc] (D2d) {} node[classlabel] {\(D_{2d}\)}; &
    \node[classcirc] (D3h) {} node[classlabel] {\(D_{3h}\)}; &
    \node[classcirc, dashed] (O)   {} node[classlabel] {\(O_{}\)};   &
    \node[classcirc] (D4)  {} node[classlabel] {\(D_{4}\)};  &

    \node[classcirc] (D6)  {} node[classlabel] {\(D_{6}\)};  &
    \node[classcirc, dashed] (Oh)  {} node[classlabel] {\(O_{h}\)};  &
    \node[classcirc] (D4h) {} node[classlabel] {\(D_{4h}\)}; &
    \node[classcirc] (D6h) {} node[classlabel] {\(D_{6h}\)}; \\
  };


  \node[cross] at ($(C1)+(4mm,0)$) {};

  
  \node[cross] at ($(C2)+(4mm,0)$) {};
  \node[cross] at ($(C2)-(4mm,0)$) {};


  \node[cross] at ($(C3)+(  0:4mm)$) {};
  \node[cross] at ($(C3)+(120:4mm)$) {};
  \node[cross] at ($(C3)+(240:4mm)$) {};


  \node[cross] at ($(Ci)+(4mm,0)$) {};
  \node[round] at ($(Ci)-(4mm,0)$) {};


  \node[cross] at ($(Cs)+(4mm,0)$) {};
  \node[round] at ($(Cs)+(4mm,0)$) {};


  \node[cross] at ($(C3i)+(  0:4mm)$) {};
  \node[cross] at ($(C3i)+(120:4mm)$) {};
  \node[cross] at ($(C3i)+(240:4mm)$) {};
  \node[round] at ($(C3i)+( 60:4mm)$) {};
  \node[round] at ($(C3i)+(180:4mm)$) {};
  \node[round] at ($(C3i)+(300:4mm)$) {};


  \node[cross] at ($(C2h)+(4mm,0)$) {};
  \node[cross] at ($(C2h)-(4mm,0)$) {};
  \node[round] at ($(C2h)+(4mm,0)$) {};
  \node[round] at ($(C2h)-(4mm,0)$) {};


  \node[cross] at ($(D2)+( 20:4mm)$) {};
  \node[cross] at ($(D2)+(200:4mm)$) {};
  \node[round] at ($(D2)+(160:4mm)$) {};
  \node[round] at ($(D2)+(340:4mm)$) {};


  \foreach \x in {0, 120, 240} {
    \node[cross] at ($(D3d)+({\x+15}:4mm)$) {};
    \node[cross] at ($(D3d)+({\x-15}:4mm)$) {};
  }


  \foreach \x in {0, 180} {
    \node[cross] at ($(C2v)+({\x+15}:4mm)$) {};
    \node[cross] at ($(C2v)+({\x-15}:4mm)$) {};
  }


  \foreach \x in {0, 180} {
    \node[cross] at ($(D2h)+({\x+15}:4mm)$) {};
    \node[cross] at ($(D2h)+({\x-15}:4mm)$) {};
    \node[round] at ($(D2h)+({\x+15}:4mm)$) {};
    \node[round] at ($(D2h)+({\x-15}:4mm)$) {};
  }


  \foreach \x in {0, 120, 240} {
    \node[cross] at ($(D3)+({\x+15}:4mm)$) {};
    \node[round] at ($(D3)+({\x-15}:4mm)$) {};
  }


  \foreach \x in {0, 90, 180, 270} {
    \node[cross] at ($(C4)+(\x:4mm)$) {};
  }


  \foreach \x in {0, 60, 120, 180, 240, 300} {
    \node[cross] at ($(C6)+(\x:4mm)$) {};
  }


  \foreach \x in {0, 120, 240} {
    \node[cross] at ($(D3dP)+({\x+15}:4mm)$) {};
    \node[cross] at ($(D3dP)+({\x-15}:4mm)$) {};
    \node[round] at ($(D3dP)+({\x+15+60}:4mm)$) {};
    \node[round] at ($(D3dP)+({\x-15+60}:4mm)$) {};
  }


  \node[cross] at ($(S4)+(4mm,0)$) {};
  \node[cross] at ($(S4)-(4mm,0)$) {};
  \node[round] at ($(S4)+(0,4mm)$) {};
  \node[round] at ($(S4)-(0,4mm)$) {};


  \foreach \x in {0, 120, 240} {
    \node[cross] at ($(S3)+(\x:4mm)$) {};
    \node[round] at ($(S3)+(\x:4mm)$) {};
  }


  %% TODO: T


  \foreach \x in {0, 90, 180, 270} {
    \node[cross] at ($(C4h)+(\x:4mm)$) {};
    \node[round] at ($(C4h)+(\x:4mm)$) {};
  }


  \foreach \x in {0, 60, 120, 180, 240, 300} {
    \node[cross] at ($(C6h)+(\x:4mm)$) {};
    \node[round] at ($(C6h)+(\x:4mm)$) {};
  }


  %% TODO: Th


  \foreach \x in {0, 90, 180, 270} {
    \node[cross] at ($(C4v)+(\x+15:4mm)$) {};
    \node[cross] at ($(C4v)+(\x-15:4mm)$) {};
  }



  \foreach \x in {0, 60, 120, 180, 240, 300} {
    \node[cross] at ($(C6v)+(\x+10:4mm)$) {};
    \node[cross] at ($(C6v)+(\x-10:4mm)$) {};
  }


  %% TODO: Td


  \foreach \x in {0, 180} {
    \node[cross] at ($(D2d)+({\x+15}:4mm)$) {};
    \node[round] at ($(D2d)+({\x-15}:4mm)$) {};

    \node[round] at ($(D2d)+({\x+15+90}:4mm)$) {};
    \node[cross] at ($(D2d)+({\x-15+90}:4mm)$) {};
  }


  \foreach \x in {0, 120, 240} {
    \node[cross] at ($(D3h)+({\x+15}:4mm)$) {};
    \node[cross] at ($(D3h)+({\x-15}:4mm)$) {};
    \node[round] at ($(D3h)+({\x+15}:4mm)$) {};
    \node[round] at ($(D3h)+({\x-15}:4mm)$) {};
  }


  %% TODO: O


  \foreach \x in {0, 90, 180, 270} {
    \node[cross] at ($(D4)+({\x+15}:4mm)$) {};
    \node[round] at ($(D4)+({\x-15}:4mm)$) {};
  }

  \foreach \x in {0, 60, 120, 180, 240, 300} {
    \node[cross] at ($(D6)+({\x+10}:4mm)$) {};
    \node[round] at ($(D6)+({\x-10}:4mm)$) {};
  }


  % TODO Oh


  \foreach \x in {0, 90, 180, 270} {
    \node[cross] at ($(D4h)+(\x+15:4mm)$) {};
    \node[cross] at ($(D4h)+(\x-15:4mm)$) {};
    \node[round] at ($(D4h)+(\x+15:4mm)$) {};
    \node[round] at ($(D4h)+(\x-15:4mm)$) {};
  }


  \foreach \x in {0, 60, 120, 180, 240, 300} {
    \node[cross] at ($(D6h)+({\x+10}:4mm)$) {};
    \node[cross] at ($(D6h)+({\x-10}:4mm)$) {};
    \node[round] at ($(D6h)+({\x+10}:4mm)$) {};
    \node[round] at ($(D6h)+({\x-10}:4mm)$) {};
  }
\end{tikzpicture}
\end{document}