Patient heterogeneity, in which patients can be grouped by risk of toxicity, is a design challenge in early phase dose finding trials. Carrying out independent trials for each group is a readily available approach for dose finding. However, this often leads to dose recommendations that violate the known order of toxicity risk by group, or reversals in dose recommendation. In this manuscript, trials for partially ordered groups are simulated using four approaches: independent parallel trials using the continual reassessment method (CRM), Bayesian optimal interval design, and 3 + 3 methods, as well as CRM for partially ordered groups. Multiple group order structures are considered, allowing for varying amounts of group frailty order information. These simulations find that parallel trials in the presence of partially ordered groups display a high frequency of trials resulting in reversals. Reversals occur when dose recommendations do not follow known order of toxicity risk by group, such as recommending a higher dose level in a group of patients known to have a higher risk of toxicity. CRM for partially ordered groups eliminates the issue of reversals, and simulation results indicate improved frequency of maximum tolerated dose selection as well as treating a greater proportion of trial patients at this dose compared with parallel trials. When information is available on differences in toxicity risk by patient subgroup, methods designed to account for known group ordering should be considered to avoid reversals in dose recommendations and improve operating characteristics.