Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
204 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 75 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. #26022095 | C2 | semidirect |
| 3. #26018319 | C2 | semidirect |
| 4. #26018228 | C2 | semidirect |
| 5. #26018227 | C2 | semidirect |
| 6. #26018174 | C2 | semidirect |
| 7. C89×#2171 | C2 | semidirect |
| 25. #15667958 | C8 | semidirect |
| 26. #15667956 | C8 | semidirect |
| 27. #15667955 | C8 | semidirect |
| 28. #15667953 | C8 | semidirect |
| 104. #2171 | D89 | semidirect |
| 109. C89 | #12068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022136 | 2 |
| #26022095 | 2 |
| #26018319 | 2 |
| #26018228 | 2 |
| #26018227 | 2 |
| #26018174 | 2 |
| C89×#2171 | 2 |
| #12068 | 89 |