Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
286 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26022467 | C2 | semidirect |
| 3. #26022464 | C2 | semidirect |
| 4. #26021833 | C2 | semidirect |
| 5. #26018242 | C2 | semidirect |
| 6. #26018204 | C2 | semidirect |
| 7. C89×#1341 | C2 | semidirect |
| 148. #1341 | D89 | semidirect |
| 150. C89 | #12304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031688 | 2 |
| #26022467 | 2 |
| #26022464 | 2 |
| #26021833 | 2 |
| #26018242 | 2 |
| #26018204 | 2 |
| C89×#1341 | 2 |
| #12304 | 89 |