  In this paper we prove the existence of continua of nonradial solutions for
the Lane-Emden equation. In a first result we show that there are infinitely
many global continua detaching from the curve of radial solutions with any
prescribed number of nodal zones. Next, using the fixed point index in cone, we
produce nonradial solutions with a new type of symmetry. This result also
applies to solutions with fixed signed, showing that the set of solutions to
the Lane Emden problem has a very rich and complex structure.
