We consider quantum phases of tightly-confined spin-2 bosons in an external field under the
presence of rotationally-invariant interactions. Generalizing previous treatments, we show how this
system can be mapped onto a quantum rotor model. Within the rotor framework, low-energy excitations
about fragmented states, which cannot be accessed within standard Bogoliubov theory, can
be obtained. In the spatially extended system in the thermodynamic limit there exists a mean-field
ground state degeneracy between a family of nematic states for appropriate interaction parameters.
It has been established that quantum fluctuations lift this degeneracy through the mechanism of
order-by-disorder and select either a uniaxial or square-biaxial ground state. On the other hand, in
the full quantum treatment of the analogous single-spatial mode problem with finite particle number
it is known that, due to symmetry restoring fluctuations, there is a unique ground state across the
entire nematic region of the phase diagram. Within the established rotor framework we investigate
the possible quantum phases under the presence of a quadratic Zeeman field, a problem which has
previously received little attention. By investigating wave function overlaps we do not find any
signatures of the order-by-disorder phenomenon which is present in the continuum case. Motivated
by this we consider an alternative external potential which breaks less symmetry than the quadratic
Zeeman field. For this case we do find the phenomenon of order-by-disorder in the fully quantum
system. This is established within the rotor framework and with exact diagonalization.