Because seventh chords have four notes, wouldn't it make them have more inversions than a triad?
Yes - the more notes avaiable in any chord the more inversions you can have.
An inversion is named purely by its lowest note, so since seventh chords by definition are comprised of four notes, ther will be, in rising order named from the lowest note they are roo, 1st, 2nd and 3rd inversions. The last probably sounding the weakest.
Of course with four notes, there are more voicings available as well.
Root in key C could be C E G B, C E B G, C G B E, C G E B, C B E G, or C B G E. All of which are playable on piano at least.