It is useful sometimes to study characters as related visual groups rather than as related phonemes. This is because Chinese characters are much less phonetically determined than Western scripts.
All of these characters are also semantically related.
image: a barred pair of gates. you must lift open the top bar to open them.
image: a mountain pass guarded with a sentry post. By extension: close, switch (off) 天 sky, day.
to grasp with two hands
to lift up with both hands thus by extension ascend raise promote