Concept:
We compare the first, second and third letters separately.
Step 1: First letters.
\[
B,\ E,\ I,\ _ _ _ _
\]
Alphabet positions are
\[
2,\ 5,\ 9,\ _ _ _ _
\]
Differences are
\[
+3,\ +4
\]
So the next difference is \(+5\):
\[
9+5=14
\]
The \(14^{th}\) letter is
\[
N
\]
Step 2: Second letters.
\[
A,\ D,\ H,\ _ _ _ _
\]
Positions are
\[
1,\ 4,\ 8,\ _ _ _ _
\]
Differences are
\[
+3,\ +4
\]
Next difference is \(+5\):
\[
8+5=13
\]
The \(13^{th}\) letter is
\[
M
\]
Step 3: Third letters.
\[
T,\ W,\ A,\ _ _ _ _
\]
Using cyclic alphabet order:
\[
T+3=W
\]
\[
W+4=A
\]
So next is
\[
A+5=F
\]
Step 4: Final answer.
Thus the missing group is
\[
\boxed{\text{NMF}}
\]