There are 2 train companies operating 3 routes - ICE42, ICE43, RJ63. The cheapest train costs $24 and is 2h 50min.
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There are 4 ways to travel from CGN to MHG. 1 flight, 4 buses, 2 trains and 1 by car are possible between the two areas. The by car from CGN to MHG is the cheapest. The train operated by DB running from Troisdorf to Mannheim is the fastest. The train operated by DB running from Porz-Wahn to Mannheim-Neckarstadt 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!