Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
636 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 143 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. #26033402 | C2 | semidirect |
| 2. #26032057 | C2 | semidirect |
| 3. #26022505 | C2 | semidirect |
| 4. #26022378 | C2 | semidirect |
| 5. #26022333 | C2 | semidirect |
| 6. #26022231 | C2 | semidirect |
| 7. #26022090 | C2 | semidirect |
| 8. C89×#2178 | C2 | semidirect |
| 145. #2178 | D89 | semidirect |
| 147. C89 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033402 | 2 |
| #26032057 | 2 |
| #26022505 | 2 |
| #26022378 | 2 |
| #26022333 | 2 |
| #26022231 | 2 |
| #26022090 | 2 |
| C89×#2178 | 2 |
| #33860 | 89 |