Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
906 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 155 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. #26021688 | C2 | semidirect |
| 3. #26021445 | C2 | semidirect |
| 4. #26021441 | C2 | semidirect |
| 5. #26021253 | C2 | semidirect |
| 6. #26020164 | C2 | semidirect |
| 7. C89×#2616 | C2 | semidirect |
| 155. #2616 | D89 | semidirect |
| 162. C89 | #32716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025976 | 2 |
| #26021688 | 2 |
| #26021445 | 2 |
| #26021441 | 2 |
| #26021253 | 2 |
| #26020164 | 2 |
| C89×#2616 | 2 |
| #32716 | 89 |