Indeed, not my favourite symmetry group. Most nested shapes that try to fit into this system feel constricted, weird, rigid, way too symmetrical. There is barely enough room to create recognisable figures within a sliver of a triangle, 30-60-90 degree (orange shape). And all of this surrounded by 3 mirrors. Ug. 

The whole of the nested shape must fit inside this sliver of a P6m triangle!

I tried, here are a few samples.

Farming Practices tessellation by Francine Champagne ©2014

Keep Mother Earth Clean tessellation by Francine Champagne ©2014

Boycott Russian Vodka tessellation by Francine Champagne ©2014

Below is my favourite P6m tessellation, Notched Louis Cubes. It does not feel restrictive in any way! I have taken the liberty to recolour it.

Notched Louis Cubes tessellation by Francine Champagne ©2015

Flower of Life tessellation by Francine Champagne, ©2016

The above is interesting as a P6m example, but is not a true tessellation in my estimation, as it is not a recognisable figure, a nested shape. It contains negative space, just like in a wallpaper design. Same is true for the snowflake design below, more wallpaper, not really nested recognisable figures.

Snowflakes tessellation by Francine Champagne ©2014

Cheers!

Federico Giudiceandrea points out that Cheers is an anagram of Escher! Very cool.