Are S4 and D12 isomorphic?

Could you please clarify for me the specific context in which S4 and D12 are being discussed? Are they both groups, perhaps related to mathematical structures or cryptographic protocols? Assuming they are indeed groups, the question "Are S4 and D12 isomorphic?" seeks to determine if there exists a bijective homomorphism between the two groups that preserves the group operation. This means that there should be a way to map elements of S4 to elements of D12 in such a way that the group operation (e.g., multiplication or composition) behaves identically under this mapping. Do you have any additional information or specific definitions of S4 and D12 that could help us explore this question further?