subfloat - enclose a set of subfloats in a subfloat environment

Question

I am struggling in finding the correct implementation for putting my two rows of figures inside a subfloat environment. What I have now is the following:

\documentclass[english]{article}
\usepackage[demo]{graphicx}
\usepackage{subfig}

\begin{document}


\begin{figure}[t]
    \centering
    \subfloat[ ]{
        \includegraphics[width=.32\textwidth]{.png}
        \label{fig1}
    }
    \subfloat[ ]{
        \includegraphics[width=.32\textwidth]{.png}
        \label{fig:2}
    }   
    \subfloat[ ]{
        \includegraphics[width=.32\textwidth]{.png}
        \label{fig:3}
    }

    \subfloat[ ]{
        \includegraphics[width=.32\textwidth]{.png}
        \label{fig:4}
    }
    \subfloat[ ]{
        \includegraphics[width=.32\textwidth]{.png}
        \label{fig:5}
    }   
    \subfloat[ ]{
        \includegraphics[width=.32\textwidth]{.png}
        \label{fig:6}
    }

    \caption{}
    \label{fig:whatever}
\end{figure}



\end{document}

It returns the following output:

I would like to have one more level of subcaption on the row. I imagine refering each single picture in the following format: Figure 1.a.1. I tried putting them in a subfloat too, but latex returns an error on the stack. One constraint, I am forced to use the subfig package, I cannot move either to subfigure or subcaption.

EDIT: example:

Answer 1

This is basically a duplicate of this answer only using \subfloat (more or less) from here.

\documentclass[english]{article}
\usepackage[demo]{graphicx}
\usepackage{subcaption}

\DeclareCaptionSubType{subfigure}
\captionsetup[subsubfigure]{labelformat=parens,labelsep=space}
\renewcommand{\thesubfigure}{\alph{subfigure}}
\renewcommand{\thesubsubfigure}{\arabic{subsubfigure}}
\AtBeginDocument{% trial and error
  \let\oldsubsubfigure=\subsubfigure
  \renewcommand{\subsubfigure}{\expandafter\def\csname @captype\endcsname{subfigure}%
    \oldsubsubfigure}%
}

\newsavebox{\subsubfloatbox}% probably overkill
\newcommand{\subsubfloat}[2][\empty]% #1 = caption (optional), #2 = image
{\bgroup
  \captionsetup[subsubfigure]{font=footnotesize}%
  \savebox\subsubfloatbox{#2}%
  \begin{subsubfigure}[t]{\wd\subsubfloatbox}
    \usebox\subsubfloatbox
    \ifx\empty#1\relax
      \stepcounter{subsubfigure}%
    \else
      \caption{#1}%
    \fi
  \end{subsubfigure}%
\egroup}

\begin{document}


\begin{figure}[t]
\begin{subfigure}{\columnwidth}
    \centering
    \subsubfloat[]{%
        \includegraphics[width=.32\textwidth]{example-image}%
        \label{fig1}%
     }\hfil
    \subsubfloat[\label{fig:2}]{%
        \includegraphics[width=.32\textwidth]{example-image}%
    }\hfil
    \subsubfloat[\label{fig:3}]{%
        \includegraphics[width=.32\textwidth]{example-image}%
    }
\caption{}
\end{subfigure}\par
\begin{subfigure}{\columnwidth}
    \subsubfloat[\label{fig:4}]{%
        \includegraphics[width=.32\textwidth]{example-image}%
    }\hfil
    \subsubfloat[\label{fig:5}]{%
        \includegraphics[width=.32\textwidth]{example-image}%
    }\hfil
    \subsubfloat[\label{fig:6}]{%
        \includegraphics[width=.32\textwidth]{example-image}%
    }
\caption{}
\end{subfigure}
    \caption{}
    \label{fig:whatever}
\end{figure}

\end{document}