Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
298 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×C32×D89 | C2 | semidirect |
| 3. #26022033 | C2 | semidirect |
| 4. #26018434 | C2 | semidirect |
| 5. #26018432 | C2 | semidirect |
| 6. #26018430 | C2 | semidirect |
| 7. C89×#1415 | C2 | semidirect |
| 10. #19152027 | C4 | semidirect |
| 110. #1415 | D89 | semidirect |
| 111. C89 | #13615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152027 | 2 |
| C2×C32×D89 | 2 |
| #26022033 | 2 |
| #26018434 | 2 |
| #26018432 | 2 |
| #26018430 | 2 |
| C89×#1415 | 2 |
| #13615 | 89 |