You can see this in the flower image. The target image has a lot of symmetries (reflections, rotations) that also exist in the GoL ruleset. So must be a parent that also has these symmetries. Yet the found solution has none of these symmetries.
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But it does have a parent with less symmetry:
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ooooo
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.....The parent still has hor/ver mirror symmetries, and the solution rotated is also a solution. So there is a set of (in this case two) parents that is invariant under the same symmetries.
In general, a parent should still be a parent when any of the targets symmetries are applied. (But it wouldn't necessarily be the same parent).
This can be captured in a SAT by insisting that any symmetry of a solution is also a solution, which adds a lot of new constraints and no new variables, so should help with finding.