This is due to the configuration of "Swimlanes" in the Board settings. Check that and see what is configured - it looks like you are showing Swimlanes based on Stories.
@Cindy Tempel
So EONE-49 is the parent, EONE-353 is it's sub-task. Similarly with the next 2 parents. All other tickets, in the Other issues section, don't have sub-tasks. As @Pete Singleton has said, this is due to the swimlane setup that you've opted for
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