We investigate the spectral shape, the anisotropy of the wave vector distributions and the anisotropy of the amplitudes of the magnetic fluctuations in the Earth's magnetosheath within a broad range of frequencies [10(-3), 10] Hz which corresponds to spatial scales from similar to 10 to 10(5) km. We present the first observations of a Kolmogorov-like inertial range of Alfvenic fluctuations delta B-perpendicular to(2)similar to f(-5/3) in the magnetosheath flanks, below the ion cyclotron frequency f(ci). In the vicinity of f(ci), a spectral break is observed, like in solar wind turbulence. Above the break, the energy of compressive and Alfvenic fluctuations generally follows a power law with a spectral index between -3 and -2. Concerning the anisotropy of the wave vector distribution, we observe a clear change in its nature in the vicinity of ion characteristic scales: if at MHD scales there is no evidence for a dominance of a slab (k(parallel to) >> k(perpendicular to)) or 2-D (k(perpendicular to)>> k(parallel to)) turbulence, above the spectral break, (f > f(ci), kc/omega(pi) > 1) the 2-D turbulence dominates. This 2-D turbulence is observed in six selected one-hour intervals among which the average ion beta varies from 0.8 to 10. It is observed for both the transverse and compressive magnetic fluctuations, independently on the presence of linearly unstable modes at low frequencies or Alfven vortices at the spectral break. We then analyse the anisotropy of the magnetic fluctuations in a time dependent reference frame based on the field B and the flow velocity V directions. Within the range of the 2-D turbulence, at scales [1, 30]kc/omega(pi), and for any beta we find that the magnetic fluctuations at a given frequency in the plane perpendicular to B have more energy along the B x V direction. This non-gyrotropy of the fluctuations at a fixed frequency is consistent with gyrotropic fluctuations at a given wave vector, with k(perpendicular to)>> k(parallel to), which suffer a different Doppler shift along and perpendicular to V in the plane perpendicular to B.