If you want to have control over the placement of the figure floats without the floating behaviour, the use the [H]ERE float specification provided by the float package:

\documentclass{report}
\usepackage{graphicx,float}
\begin{document}
\raggedbottom
\chapter{A chapter}
\section{First section}
\subsubsection{First subsection}
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{example-image}
\caption{A figure caption}
\end{figure}
\subsubsection{Second subsection}
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
\begin{figure}[H]
\centering
\includegraphics[width=.5\linewidth]{example-image-a}
\caption{A figure caption}
\end{figure}
Phasellus rhoncus risus eu pretium luctus.
\begin{figure}[H]
\centering
\includegraphics[width=.5\linewidth]{example-image-b}
\caption{A figure caption}
\end{figure}
Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas.
\begin{figure}[H]
\centering
\includegraphics[width=.5\linewidth]{example-image-c}
\caption{A figure caption}
\end{figure}
Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin cursus nibh tellus, nec condimentum sem dignissim et.
\begin{figure}[H]
\centering
\includegraphics[width=.5\linewidth]{example-image-a}
\caption{A figure caption}
\end{figure}
Sed quis tellus non quam accumsan fermentum sit amet mollis turpis.
\begin{figure}[H]
\centering
\includegraphics[width=.8\linewidth]{example-image-b}
\caption{A figure caption}
\end{figure}
Quisque rutrum est lectus, vitae tincidunt elit rhoncus non. Integer nec suscipit urna. In eget orci tellus.
\begin{figure}[H]
\centering
\includegraphics[width=.8\linewidth]{example-image-c}
\caption{A figure caption}
\end{figure}
\subsubsection{First subsection}
Donec vel massa orci. Mauris tellus arcu, porttitor a ligula nec, pellentesque rhoncus felis.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{example-image-a}
\caption{A figure caption}
\end{figure}
Praesent vitae mauris ipsum. Donec odio lectus, fermentum eu tempor vitae, congue ultrices felis. Sed pharetra ultricies tortor non vehicula.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{example-image-b}
\caption{A figure caption}
\includegraphics[width=\linewidth]{example-image-c}
\caption{A figure caption}
\end{figure}
Nullam at tortor ut lacus consequat pellentesque. Nulla nisl odio, bibendum non risus id, tempus molestie felis.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{example-image-a}
\caption{A figure caption}
\end{figure}
Pellentesque faucibus dui ut nibh bibendum iaculis. Nam sollicitudin nisi massa. Aliquam ac sem ut nisi egestas luctus. Fusce viverra lacinia dolor vitae ultricies.
\begin{figure}[H]
\centering
\includegraphics[width=.7\linewidth]{example-image-b}
\caption{A figure caption}
\end{figure}
Integer non rhoncus odio. Vivamus tellus erat, maximus a sagittis eget, ultrices id dui.
\begin{figure}[H]
\centering
\includegraphics[width=.7\textwidth]{example-image-c}
\caption{A figure caption}
\end{figure}
\subsubsection {Second subsubsection}
\end{document}
Some things to note:
Another option that requires a little more overhead in terms of changing your code, would be to use the caption package and place the images together with their captions using \captionof{figure}. Using float allows you to retain your current layout with minimal modification.
A generic reference regarding float placement - that you should study - can be found here: How to influence the position of float environments like figure and table in LaTeX?
figure,table) if you don't want the contents to float. And know that nobody can reproduce your problem with only a code fragment. Always post a complete minimal example which can be compiled to reproduce the issue. – cfr Jun 28 '16 at 23:59