Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
922 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 1. #26030830 | C2 | semidirect |
| 2. #26030681 | C2 | semidirect |
| 3. #26030679 | C2 | semidirect |
| 4. #26019868 | C2 | semidirect |
| 5. #26019866 | C2 | semidirect |
| 6. #26019858 | C2 | semidirect |
| 7. #26019843 | C2 | semidirect |
| 8. C82×D89 | C2 | semidirect |
| 9. C89×#1709 | C2 | semidirect |
| 85. C8×D89 | D8 | semidirect |
| 124. #10623494 | #135 | semidirect |
| 150. #1709 | D89 | semidirect |
| 153. C89 | #19603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030830 | 2 |
| #26030681 | 2 |
| #26030679 | 2 |
| #26019868 | 2 |
| #26019866 | 2 |
| #26019858 | 2 |
| #26019843 | 2 |
| C82×D89 | 2 |
| C89×#1709 | 2 |
| #19603 | 89 |