Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
322 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 322 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. #26022472 | C2 | semidirect |
| 3. #26022464 | C2 | semidirect |
| 4. #26021806 | C2 | semidirect |
| 5. #26018239 | C2 | semidirect |
| 6. #26018189 | C2 | semidirect |
| 7. C89×#1339 | C2 | semidirect |
| 159. #1339 | D89 | semidirect |
| 161. C89 | #12303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031163 | 2 |
| #26022472 | 2 |
| #26022464 | 2 |
| #26021806 | 2 |
| #26018239 | 2 |
| #26018189 | 2 |
| C89×#1339 | 2 |
| #12303 | 89 |