I'm soo sorry I'm new to this form and also didnt take a tutorial to post comments or topic. Pardon me.
Also sorry to post the cost with wrong library. But I was also trying with Extjs library and that too was giving me the same problem.
But I solved the problem with the issue.
Let me tell what i did so it will help others:
Goal:
I needed a google suggestbox to be added to a extjs's window so that I can do ajax search while typing in the box.
Problem:
The problem i was having was the suggestions to the box use to appear behind the window popup.
Solutions:
The suggestbox's setPopupStyleName to be set as box.setPopupStyleName("sb-setPopup");
The css having:
.sb-setPopup{
background-color: white;
border: 4px darkblue solid;
padding-left: 2px;
padding-right: 2px;
position:absolute;
z-index: 12000;
}

The z-index: 12000; is the cache. any popup if needed above the extjs window will need the z-index: 12000 (thats my guess).
But it worked. Thanks all.