Take a look at this,
This is before importing myGroup styles is : GroupStyle1

And this is after I imported XML: (Note: New style gets created named as per attributes : GroupStyle1 outside of group)

XML :
<?xml version='1.0' encoding='UTF-8'?><eduxml xmlns:aid="http://ns.adobe.com/AdobeInDesign/4.0/" xmlns:aid5="http://ns.adobe.com/AdobeInDesign/5.0/">
<p aid:pstyle="GroupStyle1">Test Para For applying Group Style</p>
</eduxml>
If you have something, let me know... 
Best
Sunil
My guess is that style groups have been added relatively later (CS4?) than XML import (CS3), and support for them by XML import was just not considered.
I currently see these possible approaches:
- File a feature request at Uservoice.
- Rearrange the styles to follow the observed limitations of the import feature.
- Write and use a post processing script for all kinds of adjustments after the import process. That script could for example utilize XML Rules or XPath features of InDesign's XML - which is different from the ExtendScript XML that you were using in the other forum thread.
- Use a different import format - a typical approach would be an externally run XSLT producing an ICML file.
- Write a plugin to implement own extensions to the XML import.