Ordering of monomial terms

I have monomials with variables $a_1,\, a_2,\,\dots$ also their complex conjugates. I found that their order within the monomial depends on at which point I set the overline for the complex conjugate. It was impossible to order them by their index (i.e., have $a_1$ and $\bar a_1$ close together).

But now I added coefficients for the monomial terms and, because they are greek letters, they will be sorted to the end of the monomial. What causes/influences this ordering? How can I get them placed at the beginning?

Here's code for two monomials, both as LaTeX and input, showing what I am experiencing.

$\qquad \left\{a_1 \beta _1 S_{i_1},\,a_3 a_6 \beta _2 \overline{a_4} \right\}$

{Subscript[β, 1]*Subscript[a, 1]*Subscript[S, Subscript[i, 1]],
OverBar[Subscript[a, 4]]*Subscript[β, 2]*Subscript[a, 3]*Subscript[a, 6]}


I found How do I reassign canonical ordering of symbols? and adapted Simon Woods answer to my problem. The following does the trick:

reorderSymbols[expr_, symbols_List] := With[{s = symbols},
\!$$\*OverscriptBox[ SubscriptBox[\(a$$, $$#$$], $$_$$]\))&,Range[6]];