The sons of Shemaiah, the firstborn of Obed-edom [ביאור שטיינזלץ], held a unique and elevated status within their family. The primary approach among commentators is that their special designation reflects a position of authority and rule. These sons served as appointed leaders and directors over their father's household [רש״י, מצודת דוד, רלב״ג, מלבי״ם, ביאור שטיינזלץ]. They were recognized as men of great authority, entirely capable of carrying out their assigned duties because of their immense strength and capability [רלב״ג].
A contrasting perspective views their title not as a measure of administrative power, but as a mark of direct comparison to their ancestors. From this viewpoint, the sons were the exact equals of their forefathers in might. Just as previous generations in their family were highly qualified and powerful in their sacred work, these sons perfectly mirrored that same greatness [רד״ק].