You can separate it into 2 zigzags, each of which is a jagged S, hence forming the symbol for the nazi "SS"
There used to be an older and harmless symbol called Fylfot, which had its legs pointing the other way round, like 2 zeds. This was sometimes regarded as a lucky charm, and could be carved into stone or wood
In Mein Kampf, Hitler described the Nazis' new flag: "In red we see the social idea of the movement, in white the nationalistic idea, in the swastika the mission of the struggle for the victory of the Aryan man, and, by the same token, the victory of the idea of creative work, which as such always has been and always will be anti-Semitic." (pg. 496-497)
Just as a matter of interest there used to be a laundry called the Swastika Laundry in Dublin many years ago. It started trading early in the 1900's - long before the formation of the Nazis. I remember seeing the red vans with this offensive symbol on the side during my college years in the 60's. All that remains of the laundry is the chimney which has been preserved for historical reasons.
This one is from the Pulguksa Temple, probably the most famous of all Buddhist temples in Korea. Founded in 751 during the Silla Dynasty, it's been ruined twice (during the Imjin War (1592-1598) and during the Korean War (1950-1953))...the swastika symbol for Buddhism adorns the Musoljon (Hall of Silence), the largest hall in Pulguksa.
Fylfot crosses (or gammadions) appear in many Christian churches. There is a fylfot mural in Christchurch Cathedral. The traditional form more often has the armspointing clockwie, but it is by no means an unbroken rule. In particular, where it has been used in windows, the "swastika" symbol is visible from one direction regardless of the orientation within the building.
The swastika was used by the German Bauhaus school of modern design from around 1900. It was adopted by the Nazis, but initially it was shown as though it was a square, resting on a flat side. Paul Klee, who lectured at the Bauhaus, advised Hitler to turn the symbol 45° to produce an image that was less static, and much more dynamic. Hitler could see the difference and immediately endorsed Klee's suggestion.