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. #26021170 | C2 | semidirect |
| 3. #26018945 | C2 | semidirect |
| 4. #26018850 | C2 | semidirect |
| 5. #26018775 | C2 | semidirect |
| 6. #26018663 | C2 | semidirect |
| 7. C89×#1983 | C2 | semidirect |
| 8. #19152342 | C4 | semidirect |
| 9. #19152340 | C4 | semidirect |
| 22. #19151655 | C22 | semidirect |
| 24. C4×#13083558 | C22 | semidirect |
| 33. C2×C4⋊C8×C89 | C22 | semidirect |
| 36. C4×C4⋊C4×C89 | C22 | semidirect |
| 294. #1983 | D89 | semidirect |
| 300. C89 | #8510 | semidirect |
| 317. C2×C4⋊C8 | C2×D89 | semidirect |
| 322. C4×C4⋊C4 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034771 | 2 |
| #26021170 | 2 |
| #26018945 | 2 |
| #26018850 | 2 |
| #26018775 | 2 |
| #26018663 | 2 |
| C89×#1983 | 2 |
| #8510 | 89 |