  We present the discovery of three new $\beta$ Cep pulsators, three new
pulsators with frequency groupings, and frequency patterns in a B3Ib star, all
of which show pulsations with frequencies as high as about 17 d$^{-1}$, with K2
space mission photometry. Based on a Fourier analysis and iterative
pre-whitening we present a classification and evaluate the potential for
asteroseismic modelling. We include the lists of pulsation frequencies for
three new $\beta$ Cep pulsators, CD-28 12286, CD-27 10876, LS 3978, and
additional pulsation mode frequencies for the known $\beta$ Cep pulsator HD
164741. In addition we characterise the regular frequency spacing found in the
new pulsator HD 169173, and discuss its origin. We place the newly discovered
variables in a colour-magnitude diagram using parallaxes from Gaia-DR2,
showcasing their approximate location in the massive star domain. The
identified frequency lists of these multiperiodic pulsators are a good starting
point for future forward seismic modelling, after identification of at least
one pulsation frequency from high-resolution time series spectroscopy and/or
multi-colour photometry.
