G. Higman (1969) constructed a symmetric $2\textrm{-}(176,50,14)$ design with doubly transitive automorphism group $HS$ (see here for its incidence graph). Brouwer (1982) showed that this design admits a polarity with 176 absolute points, yielding an $\mathrm{SRG}(176,49,12,14)$ with automorphism group $S_8$ acting intransitively with orbits of length 8 and 168.
| Number of vertices: | $176$ |
| Diameter: | $2$ |
| Intersection array: | $\{49,36;1,14\}$ |
| Spectrum: | $49^1 5^{98} (-7)^{77}$ |
| Automorphism group: | $S_8$ |
| Distance-transitive: | No |
| Primitive |