What is the issue of class conflict in Shaw's Heartbreak House?

Class conflict is the dominant theme in Heartbreak House. In it, Shaw offers a withering indictment of the so-called leisured classes in Britain during the First World War. The play serves as a kind of allegory for the wayward direction in which the British social elite is taking the country. It's instructive that the house of the eccentric old sea-dog, Captain Shotover, is built in the shape of a ship's stern. Though grand-looking from the outside, inside it's a different story; the place is an absolute mess. Metaphorically, this could be construed as a satirical statement on the current state of Britain: a ship of fools heading nowhere with an incompetent sailor at the helm and rats in the hold.
Shaw presents the upper-class "fools" aboard this ship in an especially unflattering light. They are bone idle, decadent, and easily bored. Indeed, so perpetually gripped are they by the strangulating grasp of ennui that they yearn for the excitement of another bomb landing in Shotover's garden. The middle-classes don't come off any better. The nouveau-riche Mangan is a money-grubbing parvenu who turns out to be a penniless scoundrel. All in all, the British ship of state is as ill-served by its crew as by its captain. Only the passengers aboard continue to delude themselves that they are still set fair on their original voyage.