Let \( {{\mathfrak{X}}} \) be a class of finite groups containing a group of even order and closed under subgroups, homomorphic images, and extensions. Then each finite group possesses a maximal \( {{\mathfrak{X}}} \)-subgroup of odd index and the study of the subgroups can be reduced to the study of the so-called submaximal \( {{\mathfrak{X}}} \)-subgroups of odd index in simple groups. We prove a theorem that deduces the description of submaximal \( {{\mathfrak{X}}} \)-subgroups of odd index in an alternating group from the description of maximal \( {{\mathfrak{X}}} \)-subgroups of odd index in the corresponding symmetric group. In consequence, we classify the submaximal soluble subgroups of odd index in alternating groups up to conjugacy.

令\（{{\ mathfrak {X}}} \）是一类有限组，其中包含一组偶数阶并且在子组，同态图像和扩展名下封闭。然后，每个有限组都具有一个最大的\（{{\ mathfrak {X}}} \） -奇数索引子组，并且可以将子组的研究简化为所谓的子最大 \（{{\\ mathfrak { X}}} \）-简单组中奇数索引的子组。我们证明定理该次最大推导出的描述\（{{\ mathfrak {X}}} \）从最大的描述的交替组中的奇数索引的-subgroups \（{{\ mathfrak {X}}} \）-对应对称组中奇数索引的子组。因此，我们将奇数索引的次最大可溶子组归类为交替组，直到共轭为止。