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IGR J17091--3624 is a transient galactic black hole which has a distinct quasi-periodic variability known as `heartbeat', similar to the one observed in GRS 1915+105. In this paper, we report the results of $\sim 125$ ks \textit{AstroSat} observations of this source during the 2016 outburst. For the first time a double peaked QPO (DPQ) is detected in a few time segments of this source with a difference of $δf ~\sim12$ mHz between the two peaks. The nature of the DPQ was studied based on hardness ratios and using the static as well as the dynamic power spectrum. Additionally, a low frequency (25--48 mHz) `heartbeat' single peak QPO (SPQ) was observed at different intervals of time along with harmonics ($50-95$ mHz). Broadband spectra in the range $0.7-23$ keV, obtained with \textit{SXT} and \textit{LAXPC}, could be fitted well with combination of a thermal Comptonisation and a multicolour disc component model. During \textit{AstroSat} observation, the source was in the Soft-Intermediate State (SIMS) as observed with \textit{Swift/XRT}. We present a comparative study of the `heartbeat' state variability in IGR J17091--3624 with GRS 1915+105. Significant difference in the timing properties is observed although spectral parameters ($Γ\sim2.1-2.4$ and $T_\mathrm{max}\sim0.6-0.8$ keV) in the broad energy band remain similar. Spectral properties of segments exhibiting SPQ and DPQ are further studied using simple phase resolved spectroscopy which does not show a significant difference. Based on the model parameters, we obtain the maximum ratio of mass accretion rate in GRS 1915+105 to that in IGR J17091--3624 as $\sim25:1$. We discuss the implications of our findings and comment on the physical origin of these exotic variabilities.