The reason that many text-books don't give the exact location
of the secondary maxima, is simply because they are much harder
to calculate.
You need a lot more math to find them.

You start by calculating the intensity profile of
single-slit diffraction.
I skip the lengthy derivation here, because you can find it in any 
advanced text-book about wave optics.
The final result is Fraunhofer's diffraction equation
(see [Diffraction - Single-slit diffraction][1]):

$$I(\theta) = I_0 \left(\frac
{\sin\left(\frac{d\pi}{\lambda}\sin\theta\right)}
{\frac{d\pi}{\lambda}\sin\theta}
\right)^2 \tag{1}$$
where $d$ is the slit width, $\lambda$ is the wavelength,
and $\theta$ is the observed angle.

[![intensity profile][2]][2]  
<sub>(image from [Diffraction - single-slit diffraction][1])</sub>

By defining $x=\frac{d\pi}{\lambda}\sin\theta$,
we can write (1) in a simpler way as
$$I(\theta)=I_0\left(\frac{\sin x}{x}\right)^2 \tag{2}$$

Now it is straight-forward to find the $x$ values
of the maxima and minima:

* The primary maximum is at $x=0$.
* The minima are at $x=\pm\pi, \pm 2\pi, \pm 3\pi, \pm 4\pi, ...$
* The secondary maxima are harder to find.
  Actually there is no analytical formula,
  and they can only be found by numerical methods.
  According to [The unnormalized sinc function][3] (Table 1) they are at
  $x=\pm 1.429\ \pi, \pm 2.462\ \pi, \pm 3.470\ \pi, ...$

Transforming from $x$ back to the original variables ($d,\lambda,\theta$) we have:

* The primary maximum is at $\theta=0$.
* The minima are at $\sin\theta=\pm\frac\lambda d, \pm 2\frac\lambda d,
  \pm 3\frac \lambda d, \pm 4\frac\lambda d, ...$
* The secondary maxima are at
  $\sin\theta=\pm 1.429\frac\lambda d, \pm 2.462\frac\lambda d, \pm 3.470\frac\lambda d, ...$

Now you can see: The secondary maxima are indeed approximately (but not exactly)
half-way between the minima.

  [1]: https://en.wikipedia.org/wiki/Diffraction#Single-slit_diffraction
  [2]: https://i.sstatic.net/fbw5X.png
  [3]: http://www.physics.usyd.edu.au/teach_res/mp/doc/math_sinc_function.pdf