Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
498 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 498 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. #26029388 | C2 | semidirect |
| 3. #26018966 | C2 | semidirect |
| 4. #26018775 | C2 | semidirect |
| 5. #26018122 | C2 | semidirect |
| 6. #26018108 | C2 | semidirect |
| 7. C89×#1982 | C2 | semidirect |
| 9. #19151985 | C4 | semidirect |
| 10. #19151962 | C4 | semidirect |
| 218. #1982 | D89 | semidirect |
| 223. C89 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031270 | 2 |
| #26029388 | 2 |
| #26018966 | 2 |
| #26018775 | 2 |
| #26018122 | 2 |
| #26018108 | 2 |
| C89×#1982 | 2 |
| #9378 | 89 |