  The discovery of multiple coexisting magnetic phases in a
crystallographically homogeneous compound Ca$_3$Co$_2$O$_6$ has stimulated an
ongoing research activity. In recent years the main focus has been on the zero
field state properties, where exceedingly long time scales have been
established. In this study we report a detailed investigation of static and
dynamic properties of Ca$_3$Co$_2$O$_6$ across the magnetic field induced
transition around 3.5 T. This region has so far been practically neglected
while we argue that in some aspects it represents a simpler version of the
transition across the $B = 0$ state. Investigating the frequency dependence of
the ac susceptibility we reveal that on the high field side ($B > 3.5$ T) the
response corresponds to a relatively narrow distribution of magnetic clusters.
The distribution appears very weakly dependent on magnetic field, with an
associated energy barrier of around 200 K. Below 3.5 T a second contribution
arises, with much smaller characteristic frequencies and a strong temperature
and magnetic field dependence. We discuss these findings in the context of
intra-chain and inter-chain clustering of magnetic moments.
