Ygtjki

I would like to straighten out the top node and the bottom node so that they create a more tidy lattice. I found this post here, but I wasn't able to follow what was going on.

I just think that my subgroup diagram can be a bit...neater. For example, here is what my book's diagram looks like. How do I get my diagram to look more like the book diagram?

documentclass[12pt]article
usepackagetikz
usetikzlibrarypositioning
usepackageamsfonts


begindocument
beginfigure
centering
newcommandmydistance.6cm
begintikzpicture[node distance=1.5cm]
titleSubgroup Diagram of $Z_12$
node(A1) $langle 12 rangle = mathbbZ_12$;
node(A2) [below left of= A1] $langle 6 rangle$;
node(A3) [right of=A2] $langle 4 rangle$;
node(A4) [below left of=A2] $langle 3 rangle$;
node(A5) [below left of=A3] $langle 2 rangle$;
node(A6) [below right of=A4] $langle 1 rangle$;

draw(A1) -- (A2);
draw(A1) -- (A3);
draw(A2) -- (A4);
draw(A2) -- (A5);
draw(A3) -- (A5);
draw(A4) -- (A6);
draw(A5) -- (A6);
endtikzpicture
captionSubgroup Diagram of $mathbbZ_12$
endfigure
enddocument

Be careful with such positioning options!

documentclass[tikz]standalone
usepackageamssymb
usetikzlibrarypositioning
begindocument
begintikzpicture[every node/.style=inner sep=1pt,node distance=1.5cm]
node(A1) $langle 12 rangle$;
node(A2) [below left of= A1] $langle 6 rangle$;
node(A3) [below right of=A1] $langle 4 rangle$;
node(A4) [below left of=A2] $langle 3 rangle$;
node(A5) [below left of=A3] $langle 2 rangle$;
node(A6) [below right of=A4] $langle 1 rangle$;
node[right=0pt of A1,inner xsep=0pt] $= mathbbZ_12$;
draw(A1) -- (A2);
draw(A1) -- (A3);
draw(A2) -- (A4);
draw(A2) -- (A5);
draw(A3) -- (A5);
draw(A4) -- (A6);
draw(A5) -- (A6);
endtikzpicture
enddocument

I love positioning but may not necessarily use it when things should be on a grid.

documentclass[12pt]article
usepackagetikz
usepackageamsfonts
titleSubgroup Diagram of $Z_12$


begindocument
beginfigure
centering
begintikzpicture
 beginscope[rotate=45,scale=1.5,transform shape,nodes=fill=white,transform
 shape=false]
 draw (0,0) grid (2,1);
 path (2,1) node (A1) $langle 12 rangle = mathbbZ_12$
 (1,1) node (A2) $langle 6 rangle$
 (0,1) node (A3) $langle 3 rangle$
 (2,0) node (A4) $langle 4 rangle$
 (1,0) node (A5) $langle 2 rangle$
 (0,0) node (A6) $langle 1 rangle$;
 endscope
endtikzpicture
captionSubgroup Diagram of $mathbbZ_12$
endfigure
enddocument

Or for Joule V ;-)

documentclass[12pt]article
usepackagetikz
usepackageamsfonts
titleSubgroup Diagram of $Z_12$


begindocument
beginfigure
centering
begintikzpicture
 beginscope[rotate=45,scale=1.5,transform shape,nodes=fill=white,transform
 shape=false]
 draw (0,0) grid (2,1);
 path (2,1) node[text width=2em] (A1) $langle 12 rangle=mathbbZ_12$
 (1,1) node (A2) $langle 6 rangle$
 (0,1) node (A3) $langle 3 rangle$
 (2,0) node (A4) $langle 4 rangle$
 (1,0) node (A5) $langle 2 rangle$
 (0,0) node (A6) $langle 1 rangle$;
 endscope
endtikzpicture
captionSubgroup Diagram of $mathbbZ_12$
endfigure
enddocument