Magnetosheath jets constitute a significant coupling effect between the solar wind (SW) and the magnetosphere of the Earth. In order to investigate the effects and forecasting of these jets, we present the first-ever statistical study of the jet production during large-scale SW structures like coronal mass ejections (CMEs), stream interaction regions (SIRs) and high speed streams (HSSs). Magnetosheath data from Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft between January 2008 and December 2020 serve as measurement source for jet detection. Two different jet definitions were used to rule out statistical biases induced by our jet detection method. For the CME and SIR + HSS lists, we used lists provided by literature and expanded on incomplete lists using OMNI data to cover the time range of May 1996 to December 2020. We find that the number and total time of observed jets decrease when CME-sheaths hit the Earth. The number of jets is lower throughout the passing of the CME-magnetic ejecta (ME) and recovers quickly afterward. On the other hand, the number of jets increases during SIR and HSS phases. We discuss a few possibilities to explain these statistical results.