Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 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. #26020538 | C2 | semidirect |
| 5. #26018373 | C2 | semidirect |
| 6. #26018372 | C2 | semidirect |
| 7. C89×#1868 | C2 | semidirect |
| 20. #19151392 | C4 | semidirect |
| 21. #19151390 | C4 | semidirect |
| 194. #1868 | D89 | semidirect |
| 197. C89 | #12969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029321 | 2 |
| #26021915 | 2 |
| #26020635 | 2 |
| #26020538 | 2 |
| #26018373 | 2 |
| #26018372 | 2 |
| C89×#1868 | 2 |
| #12969 | 89 |