Deinococcus radiodurans is unusual. 

It is not able to be classified as archaebacteria because it has peptidoglycan in its cell wall, but it also has genes that are not found in eubacteria.

Until new tests came out, people agreed that it belonged to its own phylum. Since then, scientists have discovered that it is closely related to Thermus thermophilus, another extremeophile that thrives in extreme heat.  

Although the two are very different, D. radiodurans being radiation resistant and T. thermophilius being radiation sensitive, they did probably evolve from a common bacterial ancestor. The yellow bacteria show that D. radiodurans descended from ancient bacteria that are still very similar to it today.

 Deinococcus radiodurans comes from from Greek and Roman: Greek comes in with deino meaning 'terrible', and  kokkus meaning "berry". Latin influences by the word radius which translates to "radiation," and durare meaning "surviving".  

The bacteria used to be called Micrococcus radiodurans, but the name was later changed.  

It is classified as following

Kingdom: Eubacteria

Phylum: Deinococcus- Thermus

Class: Deinococci

Order: Deinococcales

Family: Deinococcaceae

            Genus: Deinococcus Radiodurans

the image below shows D. radiodurans in comparison with all of its gram positive friends!

this cladogram shows the evolutionary relationship between different bacteria, and the common ancestors between D. radiodurans and T. thermophilus. 

http://bioweb.uwlax.edu/bio203/s2008/arnold_meag/Phylogeny.htm