There are a few conflicts in this story. One is man versus nature, first shown as the professor attempts to travel in a hot air balloon and wrecks because of a bird, and then shown as a group of people attempt to live in a civilized way on an actively volcanic island. Another conflict, resolved by the people on the island, is greed versus cooperation. As we can see in this story, the "alphabet" families have created a wonderful society that is egalitarian and free of strife. If it were not for the volcano erupting, the families could still be there, living happily.
I must say that this is one of my all-time favorite stories, perhaps because it is such a pleasant tale, with human conflicts resolved so nicely.
The main conflict of a story is the problem that effects the main characters. Other characters are directly or indirectly effected by the conflict, as well, hence the term --external. An internal conflict is a problem that the character faces within himself or herself. For example, if the character has a secret fear or insecurity, that could be an internal conflict.