Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
284 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 75 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. #26022504 | C2 | semidirect |
| 5. #26019850 | C2 | semidirect |
| 6. #26018171 | C2 | semidirect |
| 7. C89×#2241 | C2 | semidirect |
| 109. #2241 | D89 | semidirect |
| 114. C89 | #12530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022508 | 2 |
| #26022504 | 2 |
| #26022477 | 2 |
| #26019859 | 2 |
| #26019850 | 2 |
| #26018171 | 2 |
| C89×#2241 | 2 |
| #12530 | 89 |