Why are you not using the previous verse (verse 26) to aid your understanding? It says "the people of the prince that shall come shall destroy the city and the sanctuary". That is what was to be made desolate. The city and the sanctuary. As Jesus prophesied about here:
Luke 19:41 And when he was come near, he beheld the city, and wept over it, 42 Saying, If thou hadst known, even thou, at least in this thy day, the things which belong unto thy peace! but now they are hid from thine eyes. 43 For the days shall come upon thee, that thine enemies shall cast a trench about thee, and compass thee round, and keep thee in on every side, 44 And shall lay thee even with the ground, and thy children within thee; and they shall not leave in thee one stone upon another; because thou knewest not the time of thy visitation.
And here (Matt 24:15-22 and Mark 13:14-20 are parallel accounts of this):
Luke 21:5 And as some spake of the temple, how it was adorned with goodly stones and gifts, he said,
6 As for these things which ye behold, the days will come, in the which there shall not be left one stone upon another, that shall not be thrown down.7 And they asked him, saying, Master, but when shall these things be? and what sign will there be when these things shall come to pass?
20 And when ye shall see Jerusalem compassed with armies, then know that the desolation thereof is nigh. 21 Then let them which are in Judaea flee to the mountains; and let them which are in the midst of it depart out; and let not them that are in the countries enter thereinto. 22 For these be the days of vengeance, that all things which are written may be fulfilled. 23 But woe unto them that are with child, and to them that give suck, in those days! for there shall be great distress in the land, and wrath upon this people. 24 And they shall fall by the edge of the sword, and shall be led away captive into all nations: and Jerusalem shall be trodden down of the Gentiles, until the times of the Gentiles be fulfilled.
It is not necessary for this to have been fulfilled within the 70th week because this is speaking of the consummation or end result of what would occur during the 70th week. It's because of the Jews overall rejection of Christ that He rendered their temple spiritually desolate during the 70th week (Matt 23:37-38) and determined that their city and temple would be made physically desolate because of that as well.
Matt 23:37 O Jerusalem, Jerusalem, thou that killest the prophets, and stonest them which are sent unto thee, how often would I have gathered thy children together, even as a hen gathereth her chickens under her wings, and ye would not! 38 Behold, your house is left unto you desolate.