The glacier is not floating, it is supported completely on the bottom of the lake. The incredible thing is that the depth reaches up to 110m. The biggest icebergs that are found floating in the lake detach from underneath and pop up like submarines - they are not broken by the impact of falling.
The level of the lake is only 165m above sea level. You have beech trees similar to the ones found in New Zealand. The Glacier is one of the few "stable" glaciers in the world, meaning that for the last 90 years it has been roughly the same size.