Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
782 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 782 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 |
|---|---|---|
| 1. #26029293 | C2 | semidirect |
| 3. #26020197 | C2 | semidirect |
| 4. #26018138 | C2 | semidirect |
| 5. C4×#99×C89 | C2 | semidirect |
| 13. #19151518 | C4 | semidirect |
| 14. #19151515 | C4 | semidirect |
| 16. #19151510 | C4 | semidirect |
| 17. #19151507 | C4 | semidirect |
| 34. C2×#13083558 | D4 | semidirect |
| 157. C2×C4×C89 | #104 | semidirect |
| 223. C4×#99 | D89 | semidirect |
| 225. C89 | #9010 | semidirect |
| 394. C2×C4 | #15667940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029293 | 2 |
| #26023467 | 2 |
| #26020197 | 2 |
| #26018138 | 2 |
| C4×#99×C89 | 2 |
| #9010 | 89 |