The reference to the power of Satan should be seen in connection to this destruction at the hands of the secret combination:
Helaman 6:25-29
25 Now behold, it is these secret oaths and covenants which Alma commanded his son should not go forth unto the world, lest they should be a means of bringing down the people unto destruction.
26 Now behold, those secret oaths and covenants did not come forth unto Gadianton from the records which were delivered unto Helaman; but behold, they were put into the heart of Gadianton by that same being who did entice our first parents to partake of the forbidden fruit—
27 Yea, that same being who did plot with Cain, that if he would murder his brother Abel it should not be known unto the world. And he did plot with Cain and his followers from that time forth.
28 And also it is that same being who put it into the hearts of the people to build a tower sufficiently high that they might get to heaven. And it was that same being who led on the people who came from that tower into this land; who spread the works of darkness and abominations over all the face of the land, until he dragged the people down to an entire destruction, and to an everlasting hell.
29 Yea, it is that same being who put it into the heart of Gadianton to still carry on the work of darkness, and of secret murder; and he has brought it forth from the beginning of man even down to this time.
The force that destroyed the Nephites was not war. Mormon explicitly notes that there were no wars at this time. Nevertheless, the government has been destroyed. The cause of the destruction was the secret combinations and their connection to the power of Satan.