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Let $F$ be a field of characteristic $p$ at least 5. We study the Loewystructures of Specht modules in the principal block of $F\Sigma_{3p}$. We showthat a Specht module in the block has Loewy length at most 4 and compositionlength at most 14. Furthermore, we classify which Specht modules have Loewylength 1, 2, 3, or 4, produce a Specht module having 14 composition factors,describe the second radical layer and the socle of the reducible Spechtmodules, and prove that if a Specht module corresponds to a partition that is$p$-regular and $p$-restricted then the head of the Specht module does notextend the socle.

On the structure of Specht modules in the principal block of $F\Sigma_{3p}$