Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
692 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #26018980 | C2 | semidirect |
| 5. #26018765 | C2 | semidirect |
| 6. #26018764 | C2 | semidirect |
| 7. C89×#1559 | C2 | semidirect |
| 9. #19152333 | C4 | semidirect |
| 10. Q8×Dic178 | C4 | semidirect |
| 214. #1559 | D89 | semidirect |
| 218. C89 | #8492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034663 | 2 |
| #26021083 | 2 |
| #26018980 | 2 |
| #26018886 | 2 |
| #26018765 | 2 |
| #26018764 | 2 |
| C89×#1559 | 2 |
| #8492 | 89 |