Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26018314 | C2 | semidirect |
| 5. #26018313 | C2 | semidirect |
| 6. #26018312 | C2 | semidirect |
| 7. C89×#1366 | C2 | semidirect |
| 125. #1366 | D89 | semidirect |
| 126. C89 | #11956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030765 | 2 |
| #364×D89 | 2 |
| #26018314 | 2 |
| #26018313 | 2 |
| #26018312 | 2 |
| C89×#1366 | 2 |
| #11956 | 89 |