Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. #26033242 | C2 | semidirect |
| 3. #26022316 | C2 | semidirect |
| 4. #26022294 | C2 | semidirect |
| 5. C16×Dic178 | C2 | semidirect |
| 6. Q32×Dic89 | C2 | semidirect |
| 8. C89×#2247 | C2 | semidirect |
| 119. #2247 | D89 | semidirect |
| 125. C89 | #33960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033242 | 2 |
| #26022514 | 2 |
| #26022316 | 2 |
| #26022294 | 2 |
| C16×Dic178 | 2 |
| Q32×Dic89 | 2 |
| C4×D1424 | 2 |
| C89×#2247 | 2 |
| #33960 | 89 |