Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
326 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #26018423 | C2 | semidirect |
| 7. #533×C89 | C4 | semidirect |
| 9. #491×C89 | C4 | semidirect |
| 13. C2×#97×C89 | C4 | semidirect |
| 101. C89 | #13594 | semidirect |
| 102. #533 | Dic89 | semidirect |
| 104. #491 | Dic89 | semidirect |
| 109. C2×#97 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021917 | 2 |
| #26018423 | 2 |
| C89×#3135 | 2 |
| #13594 | 89 |