Geodesic
Intermediate subgroups in the unitary group over the skew field of quaternions
Zapiski Nauchnykh Seminarov POMI, Integral lattices and finite linear groups, Tome 116 (1982), pp. 96-101

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We give a description of the lattice of those subgroups of the unitary group over the skew field of quaternions which contain the diagonal matrices (intermediate subgroups). It is shown that this lattice is finite. A condition for conjugacy of intermediate subgroups is found. 
@article{ZNSL_1982_116_a9,
     author = {S. L. Krupetskii},
     title = {Intermediate subgroups in the unitary group over the skew field of quaternions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {96--101},
     publisher = {mathdoc},
     volume = {116},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a9/}
}
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S. L. Krupetskii. Intermediate subgroups in the unitary group over the skew field of quaternions. Zapiski Nauchnykh Seminarov POMI, Integral lattices and finite linear groups, Tome 116 (1982), pp. 96-101. http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a9/