Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
480 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26021834 | C2 | semidirect |
| 2. #26021827 | C2 | semidirect |
| 3. #26021708 | C2 | semidirect |
| 5. #26020956 | C2 | semidirect |
| 7. #26020491 | C2 | semidirect |
| 8. #26020473 | C2 | semidirect |
| 9. C89×#1837 | C2 | semidirect |
| 148. #1837 | D89 | semidirect |
| 149. C89 | #32702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021834 | 2 |
| #26021827 | 2 |
| #26021708 | 2 |
| #26021539 | 2 |
| #26020956 | 2 |
| #26020615 | 2 |
| #26020491 | 2 |
| #26020473 | 2 |
| C89×#1837 | 2 |
| #32702 | 89 |