Whether evil or good, group members have certain things in common. Invent a symbol or traditional colors, and whether anything is given upon joining, such as a tattoo or medallion. These can cause quick reactions among characters and are a fast way to reveal who someone is. Every group wants something. Knowing their objective is crucial. We must also define the current state of their goals, so we know how far or close they are and how they feel about this.
Sometimes a group’s goal is an object they can hold in their hand, like treasure or a device, but only a few may be able to literally do so. If the object has religious or supernatural significance, then obtaining, recovering, or protecting it can be a goal, but additional motives may apply.
What will the group do once the coveted item is obtained? Use it for something or just possess it? The latter isn’t particularly interesting. Money is typically used to buy other things, but members could have different plans for their share of the loot, assuming it’s not seen as belonging to the group. If it’s divvied up, the group may disband unless a desire for more keeps them together. If it’s an item to only possess and not use, why will the group stay together after getting it? They might need other reasons, such as undertaking missions. This is true of a good group that wants to confiscate dangerous items and prevent usage by evil groups.
Land can be great appeal for security, strategy, or to control assets like a mine. A religion’s followers may seek to control and preserve a holy site or use it to interact with a god; a real-life example is the Middle East conflict over Jerusalem. Using territory as a group’s goals is problematic because disputes over land are typically between sovereign powers or settlements, not groups that, by their nature, might be more mobile. The solution is to having them working to benefit a power through that acquisition. They can be officially sanctioned (or not) by that power, able to perform acts the power can’t do openly. A group can also deliberately destroy diplomacy to cause war.
While power can be a group’s goal, it’s usually a means to an end. It’s a cliché of poor storytelling for a villain (or his henchmen) to want nothing more. It makes them cartoonish. Make sure there’s a more complex goal than this, as power only works in the short-term, such as ensuring the survival of the group or individuals within it.
Many groups have philosophical or religious reasons for existing. They want to uphold the virtues they’ve learned. This can mean either promoting those ideas or destroying those who defy them. Intolerance is a staple of humanity; an invented species can be different, which can allow us to comment on this aspect of humans. Whether good or evil, such groups and their members are often willing to risk their lives for the cause.
We may need gods and religions for this, but general-outlook philosophies can work. Examples of the latter can include believing in equal rights (for all genders, races, and more), abolishing slavery, spreading democracy, and ending the abuse by aristocracies. We may have philosophers like Plato or Socrates who have imagined ideal states that inspire groups. The advantage of using gods as inspiration is that each will have a vision their followers support and which can become the basis of multiple groups, which is easy with a pantheon where the gods are divided by their chief areas of concern. But consider how many religions and groups arose on Earth, with a single god.