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We investigate here all the possible invariant metric functions under theaction of various kinds of semi-direct product Poincar\'e subgroups and theirdeformed partners. The investigation exhausts the possible theoreticalframeworks for the spacetime realization of Cohen-Glashow's very specialrelativity and the deformation very special relativity approach byGibbons-Gomis-Pope. Within Finsler-Minkowski type of spacetime, we find thatthe spacetime emerge a Finsler type of geometry in most cases both for undermedPoincar\'e subgroup and for deformed one. We give an explanation that therotation operation should be kept even in a Lorentz violating theory fromgeometrical 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 themetric function vary with a freedom of arbitrary function of the specifiedcombination of variables. The only principle for choosing the correct geometryfrom the family can only be the dynamical behavior of physics in the spacetime.

The Finsler Type of Space-time Realization of Deformed Very Special Relativity