Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
656 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26020231 | C2 | semidirect |
| 3. #26020013 | C2 | semidirect |
| 4. #26018077 | C2 | semidirect |
| 5. #26018077 | C2 | semidirect |
| 6. #26018073 | C2 | semidirect |
| 7. C89×#1270 | C2 | semidirect |
| 239. #1270 | D89 | semidirect |
| 240. C89 | #7612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022739 | 2 |
| #26020231 | 2 |
| #26020013 | 2 |
| #26018077 | 2 |
| #26018073 | 2 |
| C89×#1270 | 2 |
| #7612 | 89 |