Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
628 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 127 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. C89⋊#2104 | C2 | semidirect |
| 2. #26021429 | C2 | semidirect |
| 3. #26021419 | C2 | semidirect |
| 5. #26020711 | C2 | semidirect |
| 6. #26020666 | C2 | semidirect |
| 7. #26020358 | C2 | semidirect |
| 8. #26020327 | C2 | semidirect |
| 197. C89 | #32701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89⋊#2104 | 2 |
| #26021429 | 2 |
| #26021419 | 2 |
| #26020795 | 2 |
| #26020711 | 2 |
| #26020666 | 2 |
| #26020358 | 2 |
| #26020327 | 2 |
| C89×#2022 | 2 |
| #32701 | 89 |