Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
676 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26029297 | C2 | semidirect |
| 3. #26020197 | C2 | semidirect |
| 4. #26020163 | C2 | semidirect |
| 5. #26018741 | C2 | semidirect |
| 6. #26018140 | C2 | semidirect |
| 7. C89×#1282 | C2 | semidirect |
| 12. #19151756 | C4 | semidirect |
| 13. #19151751 | C4 | semidirect |
| 15. #19151739 | C4 | semidirect |
| 16. #19151734 | C4 | semidirect |
| 296. #1282 | D89 | semidirect |
| 297. C89 | #9037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029474 | 2 |
| #26029297 | 2 |
| #26020197 | 2 |
| #26020163 | 2 |
| #26018741 | 2 |
| #26018140 | 2 |
| C89×#1282 | 2 |
| #9037 | 89 |