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. #26018960 | C2 | semidirect |
| 3. #26018881 | C2 | semidirect |
| 4. #26018830 | C2 | semidirect |
| 5. #26018804 | C2 | semidirect |
| 6. #26018799 | C2 | semidirect |
| 7. C89×#1496 | C2 | semidirect |
| 9. #19152334 | C4 | semidirect |
| 11. #19152323 | C4 | semidirect |
| 13. #19152268 | C4 | semidirect |
| 14. #19152263 | C4 | semidirect |
| 271. #1496 | 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 |
|---|---|
| #26034717 | 2 |
| #26018960 | 2 |
| #26018881 | 2 |
| #26018830 | 2 |
| #26018804 | 2 |
| #26018799 | 2 |
| C89×#1496 | 2 |
| #8503 | 89 |