Four homologous mesogens of the hexakis(n-alkoxy)triphenylene series (HATn, n=4,6,9,11), have been doped with the one electron oxidant NOBF4, and the electrical conductivity measured as a function of frequency in the hexagonal columnar D-h phase. The limiting low-frequency conductivities both parallel, sigma(parallel to), and perpendicular, sigma(perpendicular to), to the column axes decrease exponentially with increasing side-chain length. The value of all decreases by three orders of magnitude in going from n=4 to n=11. This can be understood in terms of an increasing degree of disorder in the packing of molecules in the columns. The decrease of sigma(perpendicular to) by some two orders of magnitude can be attributed to the increase in the distance between the columns.