Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
218 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26018318 | C2 | semidirect |
| 5. #26018317 | C2 | semidirect |
| 6. #26018317 | C2 | semidirect |
| 7. C89×#1368 | C2 | semidirect |
| 108. #1368 | D89 | semidirect |
| 109. C89 | #12030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022053 | 2 |
| #26019006 | 2 |
| #334×D89 | 2 |
| #26018318 | 2 |
| #26018317 | 2 |
| C89×#1368 | 2 |
| #12030 | 89 |