Geodesic
The arrangement of the long and short root subgroups in the Chevalley group of type~$G_2$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 7, Tome 272 (2000), pp. 273-285

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We describe subgroups generated by a long and short root subgroups in a Chevalley group of type $G_2$ and classify orbits of the group acting on such pairs by simultaneous conjugation. 
@article{ZNSL_2000_272_a16,
     author = {V. V. Nesterov},
     title = {The arrangement of the long and short root subgroups in the {Chevalley} group of type~$G_2$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {273--285},
     publisher = {mathdoc},
     volume = {272},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_272_a16/}
}
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V. V. Nesterov. The arrangement of the long and short root subgroups in the Chevalley group of type~$G_2$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 7, Tome 272 (2000), pp. 273-285. http://geodesic.mathdoc.fr/item/ZNSL_2000_272_a16/