Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
358 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26022026 | C2 | semidirect |
| 3. #26022024 | C2 | semidirect |
| 6. #26018348 | C2 | semidirect |
| 7. C89×#1382 | C2 | semidirect |
| 12. C2×#15667951 | C4 | semidirect |
| 13. C2×C16×D89 | C4 | semidirect |
| 146. #1382 | D89 | semidirect |
| 147. C89 | #12832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152014 | 2 |
| #26022026 | 2 |
| #26022024 | 2 |
| #26020299 | 2 |
| #26020295 | 2 |
| #26018348 | 2 |
| C89×#1382 | 2 |
| #12832 | 89 |