Extensions of a group

I want to understand the groups of order 16, in order to construct them I have to understand the extension problem. So I am currently studying chapter 7 of Rotman.

The groups of order 16 are:
C16
C8 x C2
C4 x C4
C4 x C2 x C2
C2 x C2 x C2 x C2
D16
Q16
QD16
D8 x C2
Q8 x C2
C8 : C2
C4 : C4
(C4 x C2) : C2 (a)
(C4 x C2) : C2 (b)

At this moment I can construct
C16
C8 x C2
C4 x C4
C4 x C2 x C2
C2 x C2 x C2 x C2
D16
D8 x C2
Q8 x C2
C8 : C2
C4 : C4

Work to do on:
Q16
QD16
(C4 x C2) : C2 (a)
(C4 x C2) : C2 (b)