1). The culture of the organization. What values does the organization promote? A value system that promotes various forms of racism or ethnocentrism has the potential to increase the likelihood of destructive obedience. The leaders of an organization lead as much by example as anything. Does the organization operate in the open, or do much of the goings on of the organization remain hidden from view. The more hidden the activities, the less accountability of the participants for their actions, and hence a greater likelihood of engaging in destructive behaviors.
2). The legitimacy of the authority figure. Authority figures are extremely dependent upon their subordinates for their legitimacy to rule or give orders. Naturally, the military culture is one in which rank is associated with legitimacy. Orders coming from higher ranks are going to be given greater credence. Certainly there is a coercive element to be considered: failure or refusal to follow a directive from someone of higher rank can get one in deep trouble. But there's also an influential element: we have a tendency to assume that those in charge know what they are doing, hence again setting a psychological framework that encourages obedience.
3). Psychological distance from the victim. Destructive obedience is much more easily carried out if the perpetrator can distance himself or herself from the victim. This can be facilitated by deindividuation (e.g., uniforms, etc., that make one blend in with the group, thus decreasing accountability) and/or dehumanization of the victim (e.g., use of racial epithets, claims that the victims are "savages" or "have no souls" or are "sub-human", thus reducing the perpetrator's ability to empathize with the victim). Disguising victims with hoods or masks can also achieve similar effect.
4). Gradual, repetitive tasks. Destructive obedience does not occur overnight, but rather the perpetrator must be eased into increasingly brutal behaviors over a period of time. Both Milgram and Zimbardo aptly demonstrated this point with their own experimental research, and historically we've seen this point documented time and time again (the atrocities committed by the Germans during the Nazi era come most readily to mind). By gradually escalating the abuses against the victims, those who will perpetrate those abuses don't realize what's going on until they are in too deep. They become increasingly desensitized to the horrors that are going on around them, and that they too may be perpetrating.
5). Diffusion of responsibility. Destructive obedience is most easily facilitated under conditions where the perpetrators can pass the buck to someone else. Perhaps the authorities in charge give their assurances that they, rather than the perpetrators, are in charge and responsible for whatever outcomes occur. Another means of achieving that end is to compartmentalize tasks sufficiently so that one has only a small role in the abuse that is perpetrated. Some individuals in a prison camp may be merely assigned clerical duties, whereas others have some other limited role in the process of torturing or harming their victims. This provides the basis for the so-called "Nuremberg Defense" in which one can claim to be merely following orders, or simply involved in filing paperwork, taking photos, etc.
6). Provide no apparent means for escaping the situation. If the perpetrators feel suffienctly trapped in the situation, authorities are better positioned to order them to continue escalating destructive behaviors against their victims. If the perception is that there is no viable recourse but to continue doling out the abuse, then it's not terribly surprising that the perpetrators will do precisely as they are told.
In other words, horrifying actions can be committed by rather ordinary people if placed in a sufficiently extraordinary set of circumstances. "Nice girls" like Pvt. England can do horrible things. These people are likely not psychopathic monsters, contrary to prevailing opinion. Perhaps that's not the most comforting thought in the world - that any of us could potentially commit acts of evil. However, that realization should force us to take a close look at the circumstances that will most facilitate destructive obedience, and to make whatever adjustments needed to reduce the likelihood of those very behaviors. That likely will require changes in organizational culture, changes in accountability of behavior, changes in the transparency of the organization's activities.
Some food for thought.