This was actually the second flag raising that day. The first was done by the initial patrol to reach the top but it was with a smaller flag and the pictures taken of this flag raising weren't as dramatic as those of the second. In order to secure the flag from the first raising and to put up a bigger one that everyone could see - a second larger flag was sent up - and this is the flag in the photograph.
I'm not sure about the fate of all the members of the first flag raising - but one of them - who was initially, if erroneously, cited as being in the second, more popular raising was killed on the island as well.
The Flag Raising actually took place fairly early in the battle. When the Marines landed they hit beaches near one end and quickly isolated the mountain. They then took it but still had to take the upper plateau what made up the bulk of Iwo Jima.