Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26029378 | C2 | semidirect |
| 3. #26021079 | C2 | semidirect |
| 4. C4×#15667938 | C2 | semidirect |
| 5. #26018670 | C2 | semidirect |
| 6. #26018084 | C2 | semidirect |
| 7. C89×#1299 | C2 | semidirect |
| 11. #19151894 | C4 | semidirect |
| 12. #19151889 | C4 | semidirect |
| 13. #19151799 | C4 | semidirect |
| 14. #19151794 | C4 | semidirect |
| 169. D356 | #104 | semidirect |
| 222. #1299 | D89 | semidirect |
| 224. C89 | #8969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030313 | 2 |
| #26029378 | 2 |
| #26021079 | 2 |
| C4×#15667938 | 2 |
| #26018670 | 2 |
| #26018084 | 2 |
| C89×#1299 | 2 |
| #8969 | 89 |