A communication method implemented on a 3rd Generation Partnership Project (3GPP) communication network includes providing an attachment between a group member of a communication group and a group application server, detecting a detachment between the group member and the group application server, and reestablishing the attachment by the 3GPP communication network. A Mobility Management Entity (MME) may provide the attachment. A Group Communication Service Enabler Application Server (GCSE AS) or a Multipoint Service (MuSe) functionality may detect the detachment. The attachment may be reestablished according to the MuSe functionality. A group communication bearer may have a first priority level for allocating resources to the group communication bearer, and a second priority level for allocating resources to the non-group communication bearer. The second priority level may be different from the first priority level. Different Quality Control Indexes (QCIs) may be provided to the group communication bearer and the non-group communication bearer.