Four-and-twenty songs baked in a wall

Question

The list of twenty-four songs below can be partitioned. Each partition is of four songs. The six rules of partition membership are related to one another: specifically, they can be thought of in such a way as to be disjoint, in the sense that no song (not even one that's not on my list) can be in more than one partition. I invite you to find the partitions and their respective rules of membership.

• "Agony of Defeet", Parliament
• "Annie's Song", John Denver
• "Beverly Jean", Curtis Lee
• "Carry On Wayward Son", Kansas
• "Der Kommissar", After the Fire
• "Gangnam Style", Psy
• "Good Day Sunshine", Beatles
• "Goodnight Saigon", Billy Joel
• "Gospel for a New Century", Yves Tumor
• "Hasta Mañana", ABBA
• "Have a Cigar", Pink Floyd
• "I Can't Stop Loving You", Don Gibson
• "In the Still of the Night", Five Satins
• "Kids Are United!", Atari Teenage Riot
• "Lazy Eye", Goo Goo Dolls
• "MacArthur Park", Richard Harris
• "Nothing Else Matters", Metallica
• "Party in the U.S.A.", Miley Cyrus
• "Riders on the Storm", Doors
• "Some Enchanted Evening", Ezio Penza
• "Swear It Again", Westlife
• "Sweet Child of Mine", Guns N' Roses
• "The Boxer", Simon & Garfunkel
• "You Suffer", Napalm Death

(The identification of a song with a particular artist and recording does not mean to imply that that artist wrote the song or was the first to record it or that that recording is the first or authoritative version of the song. But that recording of the song is the one I used in constructing the list (and the recording can help you solve this puzzle, or all but one of them can). Note, though, that the video part of the recording is not used in this puzzle.)

Another hint, added later:

The partitioning has something to do with the songs' titles.

Another hint, added even later:

I wrote, above, that the linked-to recordings "can help you solve this puzzle, or all but one of them can". The one that can't is in the same partition as "Some Enchanted Evening".

Another hint, added even later:

Another song like "Gangnam Style" is "Stairway to Heaven", Led Zeppelin. Another song like "You Suffer" is "Bess, You Is My Woman", original cast recording.

Another hint, added even later:

Someone asked in a comment, "can I solve this by looking on the wikipedia pages of these songs or are the listening of the songs essential?" (sic). Neither of those is true: the Wikipedia pages generally don't have the information needed to solve this, but listening to the songs is certainly not essential.

Another, bigger hint (especially when coupled with the earlier hints), added even later:

The reason the recordings can help you solve this puzzle (or all but one of them can) is that they give you access to the lyrics (or all but one of them do).

Answer 1

I think the groups are the following:

Group 1: No words from the title of the song appear in the song lyrics

1) "Agony of Defeet", Parliament
2) "Annie's Song", John Denver
3) "Goodnight Saigon", Billy Joel
4) "Gospel for a New Century", Yves Tumor

Group 2: The song starts with the exact title.

1) "I Can't Stop Loving You", Don Gibson
2) "Kids Are United!", Atari Teenage Riot
3) "Some Enchanted Evening", Ezio Penza
4) "You Suffer", Napalm Death

As per hint 3, "Bess, you is my woman" is also in this group since it starts with the title.

As per hint 2, the song whose recording does NOT help is probably "You Suffer" since apparently the lyrics start with the title, but I couldn't make it out from the recording at all.

Group 3: The song ends with the exact title.

1) "Gangnam Style", Psy
2) "Nothing Else Matters", Metallica
3) "Party in the U.S.A.", Miley Cyrus
4) "Sweet Child of Mine", Guns N' Roses

As per hint 3, "Stairway to Heaven" ends with the exact title as well.

Group 4: The song starts and ends with the exact title.

1) "Good Day Sunshine", Beatles
2) "In the Still of the Night", Five Satins
3) "Riders on the Storm", Doors
4) "Beverly Jean", Curtis Lee

Note: For Beverly Jean, I couldn't find the lyrics so I couldn't confirm this, but I'm pretty sure that Curtis Lee (the main singer) starts off the song with the title (even if the background singers do not).

Group 5: The song contains some or all of the words in the title, but it does not appear exactly in the song lyrics.

1) "Carry On Wayward Son", Kansas. In the song lyrics, it is "Carry on, my wayward son".
2) "MacArthur Park", Richard Harris. In the song lyrics, it is "MacArthur's Park".
3) "Swear It Again", Westlife. In the song lyrics, it is "swear it all over again".
4) "The Boxer", Simon & Garfunkel. In the song lyrics, it is "a boxer"

Group 6: The song contains the exact title and the words appear somewhere in the middle of the song (not the beginning or end)

1) "Der Kommissar", After the Fire
2) "Hasta Mañana", ABBA
3) "Have a Cigar", Pink Floyd
4) "Lazy Eye", Goo Goo Dolls

Of course, with these groupings,

it is fairly easy to see that any song in the world will fall in one of these categories (even if the song is purely instrumental or in some other language other than English).

Answer 2

This might be a very silly guess (I hope it's allowed here), but:

The list can be partitioned based on the first letter of the title. Some letters are an "empty set", and so the rule of 4 songs per group persists. We get these groups:

- A,B,C,E (Empty)
- G,F (Empty),J (Empty),W (Empty)
- H,I,U (Empty),V (Empty)
- D,K,L,M
- R,S,O (Empty),Q (Empty),X (Empty), Z(Empty)
- N,P,T,Y

Obviously, every song in the world will only fall into one of these bins.