Ti₂Ni and the related η-carbide structure are known to exhibit various intriguing physical properties. The Ti₂Ni structure with the cubic space group Fd3̅m is surprisingly complex, consisting of a unit cell with 96 metal atoms. The related η-carbide compounds correspond to a filled version of the Ti₂Ni structure. Here, we report on the structure and superconductivity in the η-carbide-type suboxides Ti₄M₂O with M = Co, Rh, and Ir. We have successfully synthesized all three compounds in the single-phase form. We found all three compounds to be type-II bulk superconductors with transition temperatures of Tc = 2.7, 2.8, and 5.4 K and with normalized specific heat jumps of ΔC/γT_c = 1.65, 1.28, and 1.80 for Ti₄Co₂O, Ti₄Rh₂O, and Ti₄Ir₂O, respectively. We found that all three superconductors exhibit high upper critical fields. Particularly noteworthy in this regard is Ti₄Ir₂O with an upper critical field of μ₀H_c2(0) = 16.06 T, which exceeds by far the weak-coupling Pauli limit─widely considered as the maximal upper critical field─of μ₀H_Pauli = 9.86 T. The role of the void-filling light atom X has so far been uncertain for the overall physical properties of these materials. Herein, we have successfully grown single crystals of Ti₂Co. In contrast to the metallic η-carbide-type suboxides Ti₄M₂O, we found that Ti₂Co displays a semimetallic behavior down to 0.75 K. Below 0.75 K, we observe a broad decrease in the resistivity, which can most likely be attributed to an onset of a superconducting transition at lower temperatures. Hence, the octahedral void-filling oxygen plays a crucial role in the overall physical properties, even though its effect on the crystal structure is small. Our results indicate that the design of new superconductors by incorporation of electron-acceptor atoms may in the Ti₂Ni-type structures and other materials with crystallographic void position be a promising future approach. The remarkably high upper critical fields, in this family of compounds, may furthermore spark significant future interest.