Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
624 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 624 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. C2×#19151389 | C2 | semidirect |
| 4. #26020240 | C2 | semidirect |
| 5. C4×#100×C89 | C2 | semidirect |
| 8. C22×#13083551 | C4 | semidirect |
| 14. #19151459 | C4 | semidirect |
| 16. #19151458 | C4 | semidirect |
| 17. #19151453 | C4 | semidirect |
| 232. C4×#100 | D89 | semidirect |
| 233. C89 | #13219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025138 | 2 |
| C2×#19151389 | 2 |
| C2×#19151386 | 2 |
| #26020240 | 2 |
| C4×#100×C89 | 2 |
| #13219 | 89 |