There are 2 train companies operating 2 routes - S60, EC 150. The cheapest train costs $41 and is 3h 45min.
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There are 4 ways to travel from BTS to GRZ. 1 flight, 3 buses, 1 train and 1 by car are possible between the two areas. The by car from BTS to GRZ is the cheapest and fastest. The train operated by running from Bruck/Leitha to Graz is the most convenient.
It's important to check each mode when booking your ticket so that you can find the best method for you. The cost of each type varies differently, so be sure to use Faretrotter to keep an eye out!