Considering the distance to the Cats Eye Nebula is only 3,300 light years away, it is going to be within our own Milky Way Galaxy.
the sky
The Cats's Eye Nebula is a perfect example of a planetary nebula. See related link for a pictorial.
Earth is IN a galaxy - as is the nebula.
A Galaxy is far bigger than a nebula.
A nebula galaxy does not exist.
According to Wikipedia: Radius Core: 0.2 ly
The eye of god is a Helix nebula. Close to a Planetary nebula.
The Orion nebula is part of our own galaxy (the Milky Way). The Orion nebula is about 1500 light-years away from us. Our galaxy is about 100000 light-years across.
Not "a" - it's the name of one specific planetary nebula. You can find pictures of it in Google Images.
Galaxy
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Some nebulae that can be seen without a telescope include the Orion Nebula (M42), the Lagoon Nebula (M8), and the Andromeda Galaxy (M31). These objects are bright enough to be visible to the naked eye under dark skies.