The Doghouse is the orbiting base of the Search/Destroy Agency, mutant bounty hunters popularly known as 'Strontium Dogs'. Its name betrays its dual nature (see notes): half refuge, half prison for the despised mutant survivors of the 'norm'/mutant war of the late 22nd century. Permitted to use their strange abilities in the pursuit of (alleged) criminals, Strontium Dogs are tolerated but not liked. The Doghouse, whose only 'norm' inhabitants were traditionally police officers such as former Directors Harvey and Sydney (and, until his death, the time-displaced Viking Wulf Sternhammer), is therefore more of a utilitarian base than a home. Its facilities include somewhat rough-and-ready recreation areas, monitor screens (lots of them — they're big on screens in the Doghouse) and cells which double as torture chambers.
There are many ventilation shafts. Such bases always have them, and the shafts are always used as a secret escape route by the good guys when things turn nasty. In this case it was the Gronk who used them to bring succour to Johnny Alpha, perhaps the most famous Strontium Dog of them all, when his evil father Nelson Bunker Kreelman became director of the Agency under the name of Norman King and had Johnny imprisoned.
The Doghouse also has a recycling plant, because being an organisation full of scary mutants with big guns and short tempers doesn't mean you can't be green as well.
Following the destruction and rebuilding of the Doghouse, the newly re-established Agency hired Elwood to be its new Director.
'Doghouse' is defined in the Chambers Dictionary (10th edition) as "a place of disgrace (fig)."