My class contains
14 private methods
1 public method
Purists will tell you that the private methods could be extracted to another helper class providing accessible methods, and they could be right.
But if it makes sense to keep these utility methods inside the class, if the class is not part of a public API and is not intended to be subclassed (it could be final, for example), I don't see any problem with making some of its private methods package-protected or protected. Especially if this non-private visibility is documented, for example with the Guava annotation