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This article is a continuation of the article with the same title (seearXiv:1003.2953v1). Let {\rm $\text{HUR}_{d,t}^{G}(\mathbb P^1)$} be theHurwitz space of degree $d$ coverings of the projective line $\mathbb P^1$ withGalois group $\mathcal S_d$ and having fixed monodromy type $t$ consisting of acollection of local monodromy types (that is, a collection of conjugacy classesof permutations $\sigma$ of the symmetric group $\mathcal S_d$ acting on theset $I_d=\{1,...,d\}$). We prove that if the type $t$ contains big enoughnumber of local monodromies belonging to the conjugacy class $C$ of an oddpermutation $\sigma$ which leaves fixed $f_C\geq 2$ elements of $I_d$, then theHurwitz space {\rm $\text{HUR}_{d,t}^{\mathcal S_d}(\mathbb P^1)$} isirreducible.

Factorization semigroups and irreducible components of Hurwitz space. II