A shroud for radially encasing a turbine in a gas turbine engine is provided. The shroud comprises a carrier which defines a pin-receiving carrier bore, and a ceramic matrix composite (CMC) seal segment comprising an arcuate flange with a surface facing the turbine and a part that defines a pin-receiving seal segment bore. The seal segment bore is radially spaced from the arcuate flange by a spacing flange which extends radially outward from the arcuate flange to effect receipt within the seal segment bore of an elongated pin. The elongated pin extends through the carrier bore and the seal segment bore, and the elongated pin has a lateral cross-sectional dimension of at least three-eighths of an inch.