Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
614 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #26020351 | C2 | semidirect |
| 5. #26018106 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1826 | C2 | semidirect |
| 10. #19151533 | C4 | semidirect |
| 11. #19151524 | C4 | semidirect |
| 203. #1826 | D89 | semidirect |
| 207. C89 | #9481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26024522 | 2 |
| #26022847 | 2 |
| #26020351 | 2 |
| #26018578 | 2 |
| #26018106 | 2 |
| #26018105 | 2 |
| C89×#1826 | 2 |
| #9481 | 89 |