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We report the synthesis via an indium flux method of a novel single-crystalline compound Rh₃In_3.4Ge_3.6 that belongs to the cubic Ir₃Ge₇ structure type. In Rh₃In_3.4Ge_3.6, the In and Ge atoms choose to preferentially occupy, respectively, the 12d and 16f sites of the Im-3m space group, thus creating a colored version of the Ir₃Ge₇ structure. Like the other compounds of the Ir₃Ge₇ family, Rh₃In_3.4Ge_3.6 shows potential as a thermoelectric displaying a relatively large power factor, PF ~ 2 mW/cmK², at a temperature T ~ 225 K albeit showing a modest figure of merit, ZT = 8x10^-4, due to the lack of a finite band gap. Remarkably, band structure calculations reveal that this compound displays a complex Dirac-like electronic structure relatively close to the Fermi level. The electronic structure is composed of several Dirac type-I and type-II nodes, and even Dirac type-III nodes that result from the crossing between a flat band having nearly zero group velocity and a linearly dispersing band.