s

2

3

$X_{\alpha }$

$PSL\left(3,2\right)$ , $ASL\left(3,2\right)$

$ASL\left(3,2\right)\times {\mathbb{Z}}_2$ , $A_7$ , $S_7$

$PSL\left(3,2\right)\times S_4$ , $A_7\times A_6$ , $S_7\times S_6$ , $\left(A_7\times A_6\right):{\mathbb{Z}}_2$ ,

${\mathbb{Z}}_2^6:\left(SL\left(2,2\right)\times SL\left(3,2\right)\right)$ , $\left[2^{20}\right]:\left(SL\left(2,2\right)\times SL\left(3,2\right)\right)$

$\left|X_{\alpha }\right|$

$2^3\cdot 3\cdot 7$ , $2^6\cdot 3\cdot 7$

$2^7\cdot 3\cdot 7$ , $2^3\cdot 3^2\cdot 5\cdot 7$ ,

$2^4\cdot 3^2\cdot 5\cdot 7$

$2^6\cdot 3^2\cdot 7$ , $2^6\cdot 3^4\cdot 5^2\cdot 7$ , $2^8\cdot 3^4\cdot 5^2\cdot 7$ ,

$2^7\cdot 3^4\cdot 5^2\cdot 7$ , $2^{10}\cdot 3^2\cdot 7$ , $2^{24}\cdot 3^2\cdot 7$