  1T-TiSe$_2$ hosts a $2 \times 2 \times 2$ charge density wave (CDW) that is
known to form the state with localized domains separated by the domain walls
upon Cu intercalation. The CDW state with the domain wall network has attracted
significant interest due to its coexistence with superconductivity. Here we
present a scanning tunneling microscopy, transport and magnetic susceptibility
study of 1T-Ti$_{1-\text{x}}$Ta$_\text{x}$Se$_2$. Ta substitution for Ti atoms
allows us to perform experiments over the wide range of doping ($ 0 \leqslant
\text{x} \leqslant 0.2$), providing access to a significantly broader phase
diagram than Cu intercalation experiments. At x = 0.02, we observe a complex
network of domains and domain walls. We identify two distinct types of domain
walls and show their structure with atomic resolution. Additionally, an elusive
symmetry-breaking stripe CDW is found at the light substitution of x = 0.02. We
also measure highly substituted x = 0.2 crystals that are superconducting
despite the full collapse of the CDW order. Our results uncover rich CDW
physics in Ta-substituted 1T-TiSe2 crystals and illuminate the interplay
between the CDW and superconductivity.
