Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26022509 | C2 | semidirect |
| 2. #26022084 | C2 | semidirect |
| 4. #26018323 | C2 | semidirect |
| 5. #26018301 | C2 | semidirect |
| 6. #26018297 | C2 | semidirect |
| 7. C89×#1669 | C2 | semidirect |
| 56. #13083549 | D8 | semidirect |
| 120. #1669 | D89 | semidirect |
| 125. C89 | #12435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022509 | 2 |
| #26022084 | 2 |
| #26019607 | 2 |
| #26018323 | 2 |
| #26018301 | 2 |
| #26018297 | 2 |
| C89×#1669 | 2 |
| #12435 | 89 |