  We investigate here all the possible invariant metric functions under the
action of various kinds of semi-direct product Poincar\'e subgroups and their
deformed partners. The investigation exhausts the possible theoretical
frameworks for the spacetime realization of Cohen-Glashow's very special
relativity and the deformation very special relativity approach by
Gibbons-Gomis-Pope. Within Finsler-Minkowski type of spacetime, we find that
the spacetime emerge a Finsler type of geometry in most cases both for undermed
Poincar\'e subgroup and for deformed one. We give an explanation that the
rotation operation should be kept even in a Lorentz violating theory from
geometrical view of point. We also find that the admissible geometry for
$DTE3b$, TE(2), ISO(3) and ISO(2,1) actually consists of a family in which the
metric function vary with a freedom of arbitrary function of the specified
combination of variables. The only principle for choosing the correct geometry
from the family can only be the dynamical behavior of physics in the spacetime.
