Access to large amounts of diverse design solutions can support designers during the early stage of the design process. In this paper, we explore the efficacy of large language models (LLM) in producing diverse design solutions, investigating the level of impact that parameter tuning and various prompt engineering techniques can have on the diversity of LLM-generated design solutions. Specifically, LLMs are used to generate a total of 4,000 design solutions across five distinct design topics, eight combinations of parameters, and eight different types of prompt engineering techniques, comparing each combination of parameter and prompt engineering method across four different diversity metrics. LLM-generated solutions are compared against 100 human-crowdsourced solutions in each design topic using the same set of diversity metrics. Results indicate that human-generated solutions consistently have greater diversity scores across all design topics. Using a post hoc logistic regression analysis we investigate whether these differences primarily exist at the semantic level. Results show that there is a divide in some design topics between humans and LLM-generated solutions, while others have no clear divide. Taken together, these results contribute to the understanding of LLMs' capabilities in generating a large volume of diverse design solutions and offer insights for future research that leverages LLMs to generate diverse design solutions for a broad range of design tasks (e.g., inspirational stimuli).