There are 2 train companies operating 6 routes - IC26, ICE12, ICE20, EC62, ICE11, AZ1385. The cheapest train costs $74 and is 3h 4min.
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There are 3 ways to travel from Heidelberg to Hessisch Lichtenau. 3 trains, 4 buses and 1 driving option are possible between the two areas. The driving option from Heidelberg to Hessisch Lichtenau is the cheapest, quickest, and most convenient. The train operated by DB running from Heidelberg Hbf to Guxhagen 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!