We present an analysis of the spatial clustering of 695 Ly$alpha$-emitting galaxies (LAE) in the MUSE-Wide survey. All objects have spectroscopically confirmed redshifts in the range $3.3<z<6$. We employ the K-estimator of Adelberger et al. (2005), adapted and optimized for our sample. We also explore the standard two-point correlation function approach, which is however less suited for a pencil-beam survey such as ours. The results from both approaches are consistent. We parametrize the clustering properties by, (i) modelling the clustering signal with a power law (PL), and (ii) adopting a Halo Occupation Distribution (HOD) model. Applying HOD modeling, we infer a large-scale bias of $b_{rm{HOD}}=2.80^{+0.38}_{-0.38}$ at a median redshift of the number of galaxy pairs $langle z_{rm pair}ranglesimeq3.82$, while the PL analysis results in $b_{rm{PL}}=3.03^{+1.51}_{-0.52}$ ($r_0=3.60^{+3.10}_{-0.90};h^{-1}$Mpc and $gamma=1.30^{+0.36}_{-0.45}$). The implied typical dark matter halo (DMH) mass is $log(M_{rm{DMH}}/[h^{-1}rm{M}_odot])=11.34^{+0.23}_{-0.27}$. We study possible dependencies of the clustering signal on object properties by bisecting the sample into disjoint subsets, considering Ly$alpha$ luminosity, UV absolute magnitude, Ly$alpha$ equivalent width, and redshift as variables. We find a suggestive trend of more luminous Ly$alpha$ emitters residing in more massive DMHs than their lower Ly$alpha$ luminosity counterparts. We also compare our results to mock LAE catalogs based on a semi-analytic model of galaxy formation and find a stronger clustering signal than in our observed sample. By adopting a galaxy-conserving model we estimate that the LAEs in the MUSE-Wide survey will typically evolve into galaxies hosted by halos of $log(M_{rm{DMH}}/[h^{-1}rm{M}_odot])approx13.5$ at redshift zero, suggesting that we observe the ancestors of present-day galaxy groups.
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