The classification of groups of order $p^4$ is well known. However, different sources sometimes classify in different way. I am trying to compare, in the case $p=3$ between Burnside list (p. 100-102) http://www.gutenberg.org/files/40395/40395-pdf.pdf?session_id=730cced368b475738bfcf2c60e81ebba6fd01e04
and the smallgroups http://users.minet.uni-jena.de/~green/Coho/81gps/index.html
Now, I am trying to find a group in Burnside list which isomorphic to the group $4$ in the smallgroups. I think that it can only be the group $(viii)$, however I hope someone can check and tell me if I am right. Thanks in advance.