The explosion processes of supernovae (SNe) are imprinted in their explosion geometries. The recent discovery of several highly aspherical core-collapse SNe is significant, and studying these is regarded as being crucial in order to understand the underlying explosion mechanism. Here, we study the intrinsic polarization of 15 hydrogen-rich core-collapse SNe and explore the relation between polarization and the photometric and spectroscopic properties of these objects. Our sample shows diverse properties of the continuum polarization. Most SNe show a low degree of polarization at early phases but a sudden rise to ∼1% at certain points during the photospheric phase followed by a slow decline during the tail phase, with a constant polarization angle. The variation in the timing of peak polarization values implies diversity in the explosion geometry: some SNe have aspherical structures only in their helium cores, while in other SNe such structures reach out to a significant part of the outer hydrogen envelope with a common axis from the helium core to the hydrogen envelope. Other SNe show high polarization from early phases and a change in polarization angle around the middle of the photospheric phase. This implies that the ejecta are significantly aspherical out to the outermost layer and have multi-directional aspherical structures. Exceptionally, the Type IIL SN 2017ahn shows low polarization at both the photospheric and tail phases. Our results show that the timing of the polarization rise in Type IIP SNe is likely correlated with their brightness, velocity, and the amount of radioactive Ni produced: brighter SNe with faster ejecta velocity and a larger ⁵⁶Ni mass have more extended aspherical explosion geometries. In particular, there is a clear correlation between the timing of the polarization rise and the explosion energy; that is, the explosion asphericity is proportional to the explosion energy. This implies that the development of a global aspherical structure, such as a jet, might be the key for the realisation of an energetic SN in the mechanism of SN explosions.