Grohmann was a pioneer in exploring technically challenging mountains and is thought to have made more first ascents of Eastern Alps summits than anyone else.

In 1862, Grohman, Friedrich Simony and Edmund von Mojsvár founded the Austrian Alpine Club.

In 1875, he published a detailed map of the Dolomites (Karte der Dolomit-Alpen) and, in 1877, the travel book Wanderungen in den Dolomiten, which significantly stimulated mountain tourism in the area.

In his honor, the as yet unclimbed Sasso di Levante in the Langkofel Dolomites was renamed Grohmannspitze in 1875.

Already in 1898, 10 years before his death, the town of Urtijëi erected a monument to honor his many first ascents in the Dolomites.