  Cryptomelane is a hollandite-like material consisting of K$^+$ cations in an
$\alpha$-MnO$_2$ tunnel-like crystallographic motif. A sample with
stoichiometry K$_{1.461(4)}$Mn$_8$O$_{16}$ has been synthesised and its
magnetic properties investigated using variable-temperature magnetic
susceptibility, heat capacity, and neutron powder diffraction. Three distinct
magnetic transitions at $184$\,K, $54.5$\,K, and $24$\,K are assigned to
K$_{1.461(4)}$Mn$_8$O$_{16}$. Magnetic Bragg peaks emerge below $54.5$\,K, and
from their positions they indicate a modulated magnetic structure which is
incommensurate with the crystallographic nuclear structure. The model
consistent with the data is a dual-$\vec{k}_\mathrm{mag}$ structure with a
canted ferrimagnetic $\vec{k}_\mathrm{mag}=0$ component and an incommensurate
$\vec{k}_\mathrm{mag}=(0,0,k_z)$ [$k_z=0.36902(15)$] component, with the latter
most likely to be of the helical type formerly proposed for this material.
Below 24\,K, there is a magnetic transition, which gives rise to a different
set of magnetic Bragg peaks indicative of a highly complex magnetic structure.
