This gist shows all types of cards in jetpack compose and how to make them clickable using modifier.

cards.kt

@Composable
fun CardShower() {
    val context = LocalContext.current
    Row() {
        Card(
            modifier = Modifier
                .padding(8.dp)
                .clickable {
                    Toast
                        .makeText(context, "Filled Card Clicked", Toast.LENGTH_SHORT)
                        .show()
                }
        ) {
            Column(
                horizontalAlignment = Alignment.CenterHorizontally,
            ) {
                Image(
                    painter = painterResource(id = R.drawable.android),
                    contentDescription = "android image",
                    modifier = Modifier.size(100.dp)
                )
                Text(text = "Filled")
            }
        }

        ElevatedCard(modifier = Modifier
            .padding(8.dp)
            .clickable {
                Toast
                    .makeText(context, "Elevated Card Clicked", Toast.LENGTH_SHORT)
                    .show()
            }) {
            Column(horizontalAlignment = Alignment.CenterHorizontally) {
                Image(
                    painter = painterResource(id = R.drawable.android),
                    contentDescription = "android image",
                    modifier = Modifier.size(100.dp)
                )
                Text(text = "Elevated")
            }
        }
        OutlinedCard(modifier = Modifier
            .padding(8.dp)
            .clickable {
                Toast
                    .makeText(context, "Outlined Card Clicked", Toast.LENGTH_SHORT)
                    .show()
            }) {
            Column(horizontalAlignment = Alignment.CenterHorizontally) {
                Image(
                    painter = painterResource(id = R.drawable.android),
                    contentDescription = "android image",
                    modifier = Modifier.size(100.dp)
                )
                Text(text = "Outlined")
            }
        }
    }

}