This 'G' stands for Gräfenthal, a town in Thuringia, East Germany.
But at first I thought this mark might be Greiner & Herda, which is the only G H mark I could find in my books - but the mark was not quite the same as the most recorded mark of GH which has only three prongs and the G and H are either side of the crown, not underneath. The crown was the same graphic style apart from the number of the prongs. Greiner & Herda are a Bavarian firm from Oberkotzau, Greiner & Herda were founded in 1898 (some records state 1886). At first they were just decorators, but success led to making their own stuff. They mainly offered a range of highly decorated household items especially coffee and tea sets. The company was taken over in 1943 by Hans Neuerer and renamed Porzellanfabrik Neuerer. You can contact them as I think they still operate -
www.porzellan-selb.de.