Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
672 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26018963 | C2 | semidirect |
| 3. #26018829 | C2 | semidirect |
| 4. #26018804 | C2 | semidirect |
| 5. #26018800 | C2 | semidirect |
| 6. #26018720 | C2 | semidirect |
| 7. C89×#1535 | C2 | semidirect |
| 9. #19152333 | C4 | semidirect |
| 11. #19152327 | C4 | semidirect |
| 13. #19152269 | C4 | semidirect |
| 14. D4×Dic178 | C4 | semidirect |
| 267. #1535 | D89 | semidirect |
| 272. C89 | #8503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034725 | 2 |
| #26018963 | 2 |
| #26018829 | 2 |
| #26018804 | 2 |
| #26018800 | 2 |
| #26018720 | 2 |
| C89×#1535 | 2 |
| #8503 | 89 |