Finite Group DatabasebetaFinite Group Databasebeta← C7×ΓL(1,𝔽8)×AGL(1,𝔽13) #37524876
Order 22932.
168 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×ΓL(1,𝔽8)×D13⋊C3 | 2 |
| C7×ΓL(1,𝔽8)×#261 | 3 |
| C7×#11763981 | 3 |
| C7×#11763982 | 3 |
| C72×AGL(1,𝔽13) | 3 |
| C3×C7×AGL(1,𝔽13) | 7 |
| ΓL(1,𝔽8)×AGL(1,𝔽13) | 7 |
| C3×C4×C7×ΓL(1,𝔽8) | 13 |