Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
574 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26020326 | C2 | semidirect |
| 3. #26018253 | C2 | semidirect |
| 4. #26018250 | C2 | semidirect |
| 5. C89×#1462 | C2 | semidirect |
| 6. C2×#15667986 | C4 | semidirect |
| 8. #19151523 | C4 | semidirect |
| 12. #19151507 | C4 | semidirect |
| 15. #19151458 | C4 | semidirect |
| 226. #1462 | D89 | semidirect |
| 229. C89 | #11799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025986 | 2 |
| #26020326 | 2 |
| #26018253 | 2 |
| #26018250 | 2 |
| C89×#1462 | 2 |
| #11799 | 89 |