Intro (ind) 0:00-0:08 E minor
Chorus 0:08-0:24 C major, A major
Verse 1 0:24-0:46 A minor
Chorus 0:46-1:01 C major, A major
Verse 2 1:01-1:24 A minor
Chorus 1:24-1:40 C major, A major
Verse 3 1:40-2:01 A minor
Chorus 2:01-2:16 C major, A major
Chorus 2:16-2:30 C major, A major
Chorus 2:30-2:45 C major, A major
Chorus 2:45-3:00 C major, A major
Coda (ch) 3:00-3:13 n/a
Comments: Despite the surface-level simplicity of this children's song, the tonal and formal designs are quite sophisticated.
The introductory flamenco guitar solo is completely independent from the rest of the song (rather similar to the total non sequitur string quartet coda in  "Glass Onion").
The three verses are all in A minor; the choruses all alternate from C major to A major. Several Beatles' songs to date have pitted A against C ( "Another Girl",  "You're Going to Lose That Girl",  "Lady Madonna", and  "Birthday"), and a couple others have juxtaposed other tonalities that are also a minor third apart ( "Here There and Everywhere", and  "Lucy in the Sky With Diamonds" both employ G major and B-flat major). Others juxtapose A major with A minor ( "Things We Said Today", and  "While My Guitar Gently Weeps"), the parallel relationship of which is also used in other songs and other keys ( "Norwegian Wood" uses E major and E minor, and  "Michelle" uses F major and F minor). The play between A minor, A major, and C major specifically was used in  "Happiness is a Warm Gun", and will reappear in the Abbey Road Medley.
Four contiguous choruses ties a record for a Beatles track. And if you include the coda as a chorus (it is an extension of the chorus - but only by the synthesized trombone, played on a mellotron - while every other instrument stops), then it sets a new record.
And compared to contiguous verses (which is an extremely common formal design in Beatles music), contiguous choruses are only seldom found - and when they do appear, it's usually at the very end of the song, with the final chorus doubling as the coda: [44b] "Kansas City/Hey Hey Hey Hey" used four contiguous choruses, but they were two different choruses (Chorus #1, Chorus #1 again, Chorus #2, Chorus #2 again);  "I'm Down",  "Think For Yourself",  "Good Day Sunshine",  "It's All Too Much", and  "All You Need Is Love" all used three contiguous choruses, with the third doubling as the coda;  "Blue Jay Way" uses four contiguous choruses, with the fourth doubling as the coda;  "Cry Baby Cry" used three contiguous choruses immediately preceding a musically independent coda; and  "Savoy Truffle" used two contiguous choruses, with the second doubling as the coda.