Janet:
I hope you will find the following helpful. I've shared this army lesson a few times over the past few years, and in fact just sent this info to a new friend the other day. Welcome to the army! 
This is using the VI Corps units as an example. The 344th was also a "bastard" or separate unit. Read on...
This may also help you "picture" it. Each of the "bastard" or separate engineer units were all regiments. Each regiment has either two to three battalions, each battalion has three companies, plus HQ, H&S Co's etc. Here's a breakdown for the four units I am researching:
36th Engineer Regiment - 2826, 2827, 2828th Battalions
2826th - A, B and C Companies
2827th - D, E and F Companies
2828th - G, H and I Companies
39th Engineer Regiment - 1st and 2nd Battalions
1st - A, B and C Companies
2nd - D, E and F Companies
540th Engineer Regiment - 2832nd and 2833rd Battalions
2832nd - A, B and C Companies
2833rd - D, D, and F Companies
1108th Engineer Regiment - 48th and 235th Battalions
48th - A, B and C Companies
1108th - D, E, and F Companies
Many times companies were in the same area, but each company within a regiment could be given different assignments, so they did not necessarily work together.
A company was further broken down into the following:
1 company = 3 to 4 platoons (normal for an engineer unit)
1 platoon = 3 squads
My dad was 540th Combat Engineer Regiment (or later in the war, Group), 2833rd Battalion, H&S Company, 4th Platoon
Proud Daughter of Walter (Monday) Poniedzialek
540th Engineer Combat Regiment, 2833rd Bn, H&S Co, 4th Platoon
There's "No Bridge Too Far"