Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
246 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 77 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. #26019076 | C2 | semidirect |
| 3. #26019075 | C2 | semidirect |
| 4. #26018317 | C2 | semidirect |
| 5. #26018220 | C2 | semidirect |
| 6. #26018174 | C2 | semidirect |
| 7. C89×#1333 | C2 | semidirect |
| 27. #15667953 | C8 | semidirect |
| 47. D712 | C2×C8 | semidirect |
| 56. #13083549 | C2×C8 | semidirect |
| 60. D8×C89 | C2×C8 | semidirect |
| 114. #1333 | D89 | semidirect |
| 116. C89 | #12067 | semidirect |
| 160. D8 | C8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022126 | 2 |
| #26019076 | 2 |
| #26019075 | 2 |
| #26018317 | 2 |
| #26018220 | 2 |
| #26018174 | 2 |
| C89×#1333 | 2 |
| #12067 | 89 |