I take it there's no chance that readers of your document will become confused between three potential meanings of : (a) relational operator, (b) \colon (with asymmetric spacing), and (c) symbol for "semidirect of a group". (If there is such a chance, you better stick with \ltimes and/or \rtimes for "semidirect of a group", right?)
If that's the casethere's no chance for such confusion, you may want to set up a custom macro called, say, \sd, as follows:
\newcommand\sd{\mkern1.5mu{:}\mkern1.5mu} % "semidirect" 1.5mu is half of a thin-space. If that's not tight enough for your taste, try replacing the two instances of 1.5mu with 1mu.
Here's a comparison of various possible spacing choices:
\documentclass{article} \usepackage{array} \newcommand\sd{\mkern1.5mu{:}\mkern1.5mu} % "semidirect" \begin{document} \begin{tabular}{>{$}l<{$} >{\ttfamily}l} G\mathrel{:}H & \textbackslash mathrel (5mu) (default)\\ G\mathbin{:}H & \textbackslash mathbin (4mu) \\ G\,{:}\,H & 3mu symmetric \\ G\colon H & \textbackslash colon, 0mu/3mu asymmetric) \\ G\sd H & 1.5mu symmetric, \textbackslash sd\\ G\mathord{:}H & \textbackslash mathord (0mu)\\ \end{tabular} \end{document}