Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1140 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1140 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. #26028534 | C2 | semidirect |
| 2. #26021675 | C2 | semidirect |
| 3. #26021435 | C2 | semidirect |
| 4. #26021250 | C2 | semidirect |
| 5. C89×#1779 | C2 | semidirect |
| 6. C22×D712 | C22 | semidirect |
| 9. C2×#15667946 | C22 | semidirect |
| 10. C2×#15667934 | C22 | semidirect |
| 13. #19151361 | C22 | semidirect |
| 14. #19151361 | C22 | semidirect |
| 53. C24×C89 | D8 | semidirect |
| 122. #1779 | D89 | semidirect |
| 123. C89 | #32706 | semidirect |
| 160. C24 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028534 | 2 |
| #26021675 | 2 |
| #26021435 | 2 |
| #26021250 | 2 |
| C89×#1779 | 2 |
| #32706 | 89 |