Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
358 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 115 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.
| N | H ≅ G/N | type |
|---|---|---|
| 126. C89 | #9792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019015 | 2 |
| #26018854 | 2 |
| #26018608 | 2 |
| #26018541 | 2 |
| C2×#499×C89 | 2 |
| #9792 | 89 |