Every finite poset $P$ may be represented as a direct sum of products of directly irreducible posets, which is to say:
$P = \sum\limits_i^n \prod\limits_j^{m_i} P_{i,j}$
where the $P_{i,j}$ are connected and directly irreducible. So my question is if the group $Aut(P)$ of automorphisms of $P$ can be represented in terms of the groups $Aut(P_{i,j})$. I would appreciate any answers, or references to sources on the automorphism groups of of finite posets.