  We report on the bifurcation analysis of figure-eight choreography by
irreducible real orthogonal representations of its symmetry groups based on
variational principle of the action. There are four types of bifurcation
solutions in the sequence of the bifurcation cascade: (i) the trivial type
represented by trivial representation, (ii) the two-fold type by non-trivial
one-dimensional representation, (iii) the three-fold and (iv) the six-fold
types by two-dimensional irreducible representations. As numerical examples, we
present four new bifurcation solutions: non-symmetric choreographic solution of
the two-fold type, non-planar solution of the two-fold type, $y$-axis symmetric
solution of the three-fold type, and non-symmetric solution of the six-fold
type.
