Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
808 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26021185 | C2 | semidirect |
| 3. #26021171 | C2 | semidirect |
| 4. #26018948 | C2 | semidirect |
| 5. #26018778 | C2 | semidirect |
| 6. #26018666 | C2 | semidirect |
| 7. C89×#1527 | C2 | semidirect |
| 8. #19152342 | C4 | semidirect |
| 9. #19152340 | C4 | semidirect |
| 22. C2×C4⋊#10623494 | C22 | semidirect |
| 26. C4×C4⋊Dic89 | C22 | semidirect |
| 34. #432×C89 | C22 | semidirect |
| 35. C4×M16×C89 | C22 | semidirect |
| 297. #1527 | D89 | semidirect |
| 300. C89 | #8510 | semidirect |
| 316. #432 | C2×D89 | semidirect |
| 321. C4×M16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034771 | 2 |
| #26021185 | 2 |
| #26021171 | 2 |
| #26018948 | 2 |
| #26018778 | 2 |
| #26018666 | 2 |
| C89×#1527 | 2 |
| #8510 | 89 |