I agree with Brooks and Lawrence, in not having enough information to decide if you should break the group into two or have them work together as one team. Typically, when work is broken into different functions, one team might focus on one function, while another focuses on a second. As the leader of a department, it seems like it would be effective to have the group (team) identify critical priorities. What are the key results or accomplishments that are necessary to support the organization? Who are the internal and external customers that your department serves? What do customers need from you? I.e., how does your department provide value both inside and outside the organization?
Based on these questions, what are the key results that your department needs to accomplish? You can set SMART goals (Specific, Measurable, Achievable, Relevant and Realistic, and Timely) based on what needs to be accomplished. Which team members will be responsible for which goals? How will team members work together to make sure that goals are accomplished? Who else in the organization needs to understand and be clear about your department's goals, i.e, are there other stakeholders that rely on your outputs, or are there departments within the organization whose inputs you rely on?
When all team members are clear about the outcomes that must be created and when they buy into those outcomes, they are much more likely to work together cooperatively and with clear purpose.
If you would like to talk more about these ideas, feel free to contact me.