You can use the last code shown here to achieve what you want without using subcaption package at all.
But, since your question is specifically regarding how you can achieve your result using subcaption package, here's a solution to your problems.
Now, there are several "essential" bits missing from your code. So, let's look at them one by one:
You include only the subcaption package. It's always better to
load both the caption and the subcaption packages together, in
that order. As, caption package will allow you to customise all
sorts of float captions with great flexibility.
Instead of using \usepackage[demo]{graphicx}, you may use the
mwe package to display example images. The black boxes are
replaced by better looking grey-scale images.
The horizontal alignment of your figures & captions goes off-centre,
because you've used \centering only once for the outer figure
environment. For proper alignment, you must repeat \centering in
all 3 subfigure environments as well.
Also, it's better to use
\includegraphics[width=\textwidth]{example-image-a} after
\begin{subfigure}{0.56\textwidth} than using
\includegraphics{example-image-a}; as it will help achieving the
proper scaling of your images.
Another problem with your code, and this is a big one, is that you
are missing the mandatory empty-line between two subfigure
environments. See this for further explanation. You don't see
any difference due to the image scaling you have chosen. As an
experiment, change \begin{subfigure}{0.56\textwidth} to
\begin{subfigure}{0.2\textwidth} and see what happens. If you want
3 figures aligned vertically, one top of another, you have to
maintain the all essential empty-line between two sub-figures.
To meet your requirements, I had to add a few lines of code as follows:
%%%%%% begin: caption/subcaption setup %%%%%%
\renewcommand\thefigure{Main-\arabic{figure}}
\DeclareCaptionLabelFormat{simplab}{Figure~#2}
\DeclareCaptionFormat{nocap}{}
\DeclareCaptionSubType*{figure}
\renewcommand\thesubfigure{\arabic{subfigure}}
\captionsetup[subfigure]{%
font={normalsize},
labelfont={bf},
labelformat=simplab,
labelsep=colon,
singlelinecheck=true,
position=bottom
}%
%%%%%% end: caption/subcaption setup %%%%%%
- The first definition,
\renewcommand\thefigure{Main-\arabic{figure}}
is not absolutely essential in this case, but it helps to
differentiate the reference to the main figure (if needed in future)
from your pseudo-subfigures, since you need them to look exactly like
the main figures!
\DeclareCaptionLabelFormat{}{} & \DeclareCaptionFormat{}{} are
from the caption package; whereas, \captionsetup[subfigure]{} &
\DeclareCaptionSubType*{figure} are from the subcaption package.
For further information, please look at the package documentation of
caption & subcaption.
\DeclareCaptionFormat{nocap}{} defines a special empty-caption
format for main figure environments.
\DeclareCaptionLabelFormat{simplab}{Figure~#2} defines how the
figure labels are typeset.
\DeclareCaptionSubType*{figure} allows us to manually redefine
subfigure caption format using \renewcommand and
\renewcommand\thesubfigure{\arabic{subfigure}} redefines
\thesubfigure counter to print arabic numbers.
\captionsetup[subfigure]{} sets up the subfigure caption font size
to normalsize, label to \bfseries, label separator to colon and
label format to simplab which is defined earlier using
\DeclareCaptionFormat{}{}.
- Moreover, to hide the main figure caption, we use
format=nocap in
the \captionsetup{} of the main figure caption. The nocap format
was defined earlier using \DeclareCaptionFormat{}{}.
There's actually no real need to do this, because hiding the main caption is as simple as commenting out the \caption{} line using %. However, if the user still wants to refer to these 3 figures collectively, the main caption will have to be present and active (i.e. uncommented). Whichever is the case, I find it most practical just to define a custom empty-caption format and switch between the normal & the empty formats as needed, while retaining the entire caption line as it is, than to completely remove it. If, in future, the user decides to print the main caption, it is already there at the switch of a label format! Isn't that convenient? :) .. See it yourself by deleting format=nocap from the \captionsetup{} of the main figure caption!
I have also included the reference to main caption inside subcaptions, just to show that even though the main caption doesn't show up in the output PDF, it is very much valid/ active and its label can be referenced easily.
Here's the MWE code:
\documentclass{article}
\usepackage{graphicx}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{mwe} % for example figures!
%%%%%% begin: caption/subcaption setup %%%%%%
\renewcommand\thefigure{Main-\arabic{figure}}
\DeclareCaptionLabelFormat{simplab}{Figure~#2}
\DeclareCaptionFormat{nocap}{}
\DeclareCaptionSubType*{figure}
\renewcommand\thesubfigure{\arabic{subfigure}}
\captionsetup[subfigure]{%
font={normalsize},
labelfont={bf},
labelformat=simplab,
labelsep=colon,
singlelinecheck=true,
position=bottom
}%
%%%%%% end: caption/subcaption setup %%%%%%
\pagestyle{empty}
\begin{document}
\begin{figure}[htbp]
\centering
\vspace*{5pt}%
\hspace*{\fill}%
\begin{subfigure}{0.56\textwidth} % start subfigure 1
%\belowcaptionskip=8pt
\centering
\includegraphics[width=\textwidth]{example-image-a}%
\captionsetup{skip=12pt}%
\caption{First SUB-FLOAT (\ref{fig:demoMain})}
\label{fig:demo1}
\end{subfigure}% % end subfigure 1
\hspace*{\fill}% % empty line absolutely necessary!
\vspace*{8pt}%
\hspace*{\fill}%
\begin{subfigure}{0.56\textwidth} % start subfigure 2
%\belowcaptionskip=8pt
\centering
\includegraphics[width=\textwidth]{example-image-b}%
\captionsetup{skip=12pt}%
\caption{Second SUB-FLOAT (\ref{fig:demoMain})}
\label{fig:demo2}
\end{subfigure}% % end subfigure 2
\hspace*{\fill}% % empty line absolutely necessary!
\vspace*{8pt}%
\hspace*{\fill}%
\begin{subfigure}{0.56\textwidth} % start subfigure 3
\centering
\includegraphics[width=\textwidth]{example-image-c}%
\captionsetup{skip=12pt}%
\caption{Third SUB-FLOAT (\ref{fig:demoMain})}
\label{fig:demo3}
\end{subfigure}% % end subfigure 3
\hspace*{\fill}%
\captionsetup{skip=8pt, format=nocap}% % required to hide the figure (main) lable!
\caption{This is a main Float}
\label{fig:demoMain}
\end{figure}
\cleardoublepage
\end{document}
Here's how the output PDF looks:

Hope you find it useful! :)
\captioncommands, not subfigure at all. – David Carlisle May 31 '15 at 10:21figureenvironment caption, if I need to revert back to a more standardfigure-subfiguresetup. My answer given below sheds more light on how it allows me to revert back to a standard setup, if need be, by simply modifying the\captionsetupvariables for both thefigure&subfigureenvironments. – Amar May 31 '15 at 16:01