Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
616 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26018962 | C2 | semidirect |
| 5. #26018802 | C2 | semidirect |
| 6. #26018724 | C2 | semidirect |
| 7. C89×#1515 | C2 | semidirect |
| 9. Q8×Dic178 | C4 | semidirect |
| 10. #19152327 | C4 | semidirect |
| 13. #19152321 | C4 | semidirect |
| 15. #19152308 | C4 | semidirect |
| 256. #1515 | D89 | semidirect |
| 258. C89 | #8501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034740 | 2 |
| #26018962 | 2 |
| #26018881 | 2 |
| #26018827 | 2 |
| #26018802 | 2 |
| #26018724 | 2 |
| C89×#1515 | 2 |
| #8501 | 89 |