Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #26018138 | C2 | semidirect |
| 5. #26018106 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1297 | C2 | semidirect |
| 14. #19151462 | C4 | semidirect |
| 16. #19151460 | C4 | semidirect |
| 18. #19151449 | C4 | semidirect |
| 20. #19151445 | C4 | semidirect |
| 216. #1297 | D89 | semidirect |
| 219. C89 | #8778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023226 | 2 |
| C4×#15667926 | 2 |
| #26018588 | 2 |
| #26018138 | 2 |
| #26018106 | 2 |
| #26018105 | 2 |
| C89×#1297 | 2 |
| #8778 | 89 |