  We present the X-ray timing and spectral analysis of the new Galactic X-ray
transient Swift J1658.2-4242 observed with LAXPC and SXT instruments onboard
{\it Astrosat}. We detect prominent C-type quasi-periodic oscillations (QPOs)
of frequencies varying from $\sim 1.5$ Hz to $\sim 6.6$ Hz along with distinct
2nd harmonics and sub-harmonics. The QPO detected at $\sim 1.56$ Hz drifts to a
higher centroid frequency of $\sim 1.74$ in the course of the observation,
while the QPO detected at $\sim 6.6$\,Hz disappeared during hard flarings. The
fractional rms at the QPO and the sub-harmonic frequencies increases with
photon energy, while at the 2nd harmonic frequencies the rms seems to be
constant. In addition, we have observed soft time lag at QPO and sub-harmonic
frequencies up to a time scale of $\sim 35$ ms, however, at the 2nd harmonic
frequencies there is weak/zero time lag. We attempt spectral modeling of the
broadband data in the 0.7--25 keV band using the doubly absorbed disk plus
thermal Comptonization model. Based on the spectral and timing properties, we
identified the source to be in the hard intermediate state of black hole X-ray
binaries. To quantitatively fit the energy and frequency-dependent fractional
rms and time lag, we use a single zone fluctuation propagation model and
discuss our results in the context of that model.
