So I did some extensive research into the definitions of the genres (that is I looked them up in Wikipedia). Here's the description of Fantasy:
Fantasy is a genre that uses magic and other supernatural phenomena as a primary element of plot, theme, and/or setting. Many works within the genre take place in fictional worlds where magic is common. Fantasy is generally distinguished from science fiction in that it does not provide a logical (or pseudo logical) explanation for the scientifically impossible events that occur, though there is a great deal of overlap between the two (both are subgenres of speculative fiction).Here's the description of Science Fiction:
Science fiction is a genre of fiction. It differs from fantasy in that, within the context of the story, its imaginary elements are largely possible within scientifically established or scientifically postulated laws of nature (though some elements in a story might still be pure imaginative speculation). Exploring the consequences of such differences is the traditional purpose of science fiction, making it a "literature of ideas". Science fiction is largely based on writing rationally about alternative possibilities. The settings for science fiction are often contrary to known reality, but the majority of science fiction relies on a considerable degree of suspension of disbelief provided by potential scientific explanations to various fictional elements.
That should make everything clear. Fantasy has magic that is not scientifically explained. Science Fiction has story elements that are scientifically plausible. Now we turn to That Hideous Strength, the final book in C. S. Lewis's Space Trilogy. The previous books in the series, Out of the Silent Planet and Perelandra, are respectively set on Mars and Venus and they both feature aliens and space travel. That Hideous Strength takes place on Earth. Some members of The National Institute of Coordinated Experiments (N.I.C.E.) believe they are keeping the head of an executed man alive. Toward the end of the novel, Merlin, the wizard from Arthurian legend, who has been "sleeping" in an underground vault, makes an appearance and uses some of his talents against the people at N.I.C.E. So what is That Hideous Strength? Fantastical Science Fiction? Like many other works, including the aforementioned Starlighter, That Hideous Strength falls somewhere in that murky space between the genres.
Sorry, I don't have a good answer for how to divide the genres. The poles of the continuum appear well-defined. Second Foundation is obviously Science Fiction. Lord of the Rings is obviously Fantasy. The question is what to call that big chunk in the middle of the continuum.