the difference among "開く（あく）、開く（ひらく）、開ける（あける）"


i know that "開ける" involves subject and object, like :

> "窓を開けました"( windows opened, & implied someone did it ),

and "開く（あく）" only involves the subject, like :

> "窓が開きました" ( windows opened, & implied no one, maybe by wind blow ),

but i can't make it very clear if "開く（ひらく）" is similar or equal to "開ける（あける）"
which i found only very few examples says so.

