Training & Nutrition - Waht are good muscle groups to work the same day?

I want to know what muscle groups are good to work on the same day. Usually I work my chest and tri’s, back and arms/biceps, core just about everyday and legs on Sunday’s. I always start with 25-30 minutes on the eliptical machine and then go into my workout for the day. I typically hit the gym Monday, Tuesday, Friday, Sunday and ride on Wednesday and Thursday, occasionally skipping the gym on Saturday and or Sunday. By the way, my goal for the gym is overall fitness, burning some fat for the up coming season and just overall fitness.

Thanks!

You don't need or want to exercise a muscle group every day.
Here's my current schedule...
Sun) Bike (on the trainer)
Mon) Row ( or any other non-bike aerobic exercise)
Tue) Weight training lower body and back
Wed) off ( taking the day off after a leg day is a good idea)
Thur) Bike (intervals)
Fri) row
Sat) Weights... upper body and core

Do you feel that your current workout is not giving you any fitness?

Do you feel that your current workout is not giving you any fitness?
No I feel great on my current schedule i guess I should have included that little piece of info. I know it really depends on my own body and fitness level, but was just curious about how other people train for overall fitness. I guess i’m looking for a loose “rule of thumb” for training various muscle groups, if such thing exists.

The 'rule of thumb' is to mix it up, and not do the same thing day after day.

Chest/Tri's
Back/Bi's
Legs
Shoulders

is a typical four day plan, with abs mixed in.

Sounds like you're on the right track.

No I feel great on my current schedule i guess I should have included that little piece of info. I know it really depends on my own body and fitness level, but was just curious about how other people train for overall fitness. I guess i’m looking for a loose “rule of thumb” for training various muscle groups, if such thing exists.

I think of the reasons why exercise is so frustrating is that there aren't always perfect answers. I have seen many variations that have worked for specific people. I've tried some of them out and some worked out, some I didn't feel quite right doing. I'm sure I could see gains doing any of them, but there is a mental aspect involved.

I suppose I question you working your abs/core everyday. I feel that if you can do something 100% the next day, you haven't worked it very hard the day before. ;)

Various programs I have seen are:
Push/Pull split
Upper/lower
One group per day
Fullbody 2x/week

I personally don't like the upper/lower split because I find it difficult to attain my best efforts doing a squat and a deadlift (or chest press/pullup) in the same day. Your mileage may vary.

I used to do upper/lower, now I do push/pull and prefer that (mixed in with core).

I suppose I question you working your abs/core everyday. I feel that if you can do something 100% the next day, you haven't worked it very hard the day before. ;)
I should clarify what I mean when I say that I do abs/core everyday. Every time I go to the gym, 95% of the time I finish with about 100-200 crunches. I don’t do like a hardcore core workout everyday.