Z 3h point group

In the IR spectrum of NF3, there are four absorptions. Why is this consistent with NF3 belonging to the Qv rather than Z>3h point group ... 

Using the method outlined in Section 3.4, confirm that AII3 and AI2I6 belong to the Z)3h and Z>2h point groups, respectively. 

To describe the symmetry of a molecule in terms of one symmetry element (e.g. a rotation axis) provides information only about this property. Each of BF3 and NH3 possesses a 3-fold axis of symmetry, but their structures and overall symmetries are different BF3 is trigonal planar and NH3 is trigonal pyramidal. On the other hand, if we describe the symmetries of these molecules in terms of their respective point groups (Z>3h and C3v), we are providing information about all their symmetry elements. 

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