Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26030383 | C2 | semidirect |
| 5. #26018726 | C2 | semidirect |
| 6. #26018595 | C2 | semidirect |
| 7. C89×#1287 | C2 | semidirect |
| 192. #1287 | D89 | semidirect |
| 193. C89 | #10044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031452 | 2 |
| #26030383 | 2 |
| #26030284 | 2 |
| #26018886 | 2 |
| #26018726 | 2 |
| #26018595 | 2 |
| C89×#1287 | 2 |
| #10044 | 89 |