After studying graphic techniques and typography, he soon set out on his own path and worked as a freelance designer for several years in Prague and Berlin. He has been professionally involved in drawing and design since 2013, and in his work he seeks visual forms that respond sensitively to language. He regularly collaborates with Jakub Samek, Robert Jansa, Peter Bosák, Nana Esi, and the studio Tim+Tim.

While in Maastricht on a scholarship, Groch became intensely interested in comics and their possibilities. His collaboration with John Morgan, the founder of the publisher Abyme, led to the design of a new typeface called Sweathearts, made up of illustrated characters. Groch later published a book of cartoons featuring these characters. Curator Linda Dostálková subsequently prepared an exhibition of his screen prints titled Mothers and Daughters at PLATO Ostrava.