While I am not 100% clear you what are referring to when you state, "managing a total security package," but these positions do exist.
A CISO or CSO has to "manage a total security package" within an organization, which includes technology, policies and procedures, personnel, business processes and more. A person who will effectively fulfill one of these roles has to be extremely well-rounded in all aspects of security and motivated to continually learn and be challenged.
Since you are a systems engineer, you may be referring to a "total security package" as a holistic technical security environment. This environment would consist of access control technologies, firewalls, IDS/IPS, antivirus and more. A security administrator would be responsible for managing this type of environment, which to be clear, is different than a network administrator. A security administrator is more concerned with who is accessing company assets and what they are allowed to do with those assets. On the other hand a network administrator is responsible for monitoring the availability of the network -- the nodes and devices that make up the network -- and has to ensure that it is always up and running and performing properly.
While the security team can be made up of individuals who specialize in specific technologies and applications, the security administrator has to understand all of them, and has to ensure that they all work together in a synergist manner.
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