Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
706 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26021101 | C2 | semidirect |
| 3. #26018983 | C2 | semidirect |
| 4. #26018717 | C2 | semidirect |
| 5. #26018674 | C2 | semidirect |
| 6. #26018605 | C2 | semidirect |
| 7. C89×#1529 | C2 | semidirect |
| 266. #1529 | D89 | semidirect |
| 270. C89 | #8484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034822 | 2 |
| #26021101 | 2 |
| #26018983 | 2 |
| #26018717 | 2 |
| #26018674 | 2 |
| #26018605 | 2 |
| C89×#1529 | 2 |
| #8484 | 89 |