Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1062 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 175 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. #26028539 | C2 | semidirect |
| 3. #26021685 | C2 | semidirect |
| 4. #26021449 | C2 | semidirect |
| 5. #26021442 | C2 | semidirect |
| 6. #26021257 | C2 | semidirect |
| 7. C89×#1779 | C2 | semidirect |
| 8. C22×#13083563 | C22 | semidirect |
| 12. C2×#15667944 | C22 | semidirect |
| 13. C2×#15667937 | C22 | semidirect |
| 14. C2×#15667934 | C22 | semidirect |
| 20. #19151361 | C22 | semidirect |
| 21. #19151361 | C22 | semidirect |
| 78. C24×C89 | SD16 | semidirect |
| 166. #1779 | D89 | semidirect |
| 167. C89 | #32708 | semidirect |
| 218. C24 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028539 | 2 |
| #26028534 | 2 |
| #26021685 | 2 |
| #26021449 | 2 |
| #26021442 | 2 |
| #26021257 | 2 |
| C89×#1779 | 2 |
| #32708 | 89 |