Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
396 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 1. #26022435 | C2 | semidirect |
| 2. #26021680 | C2 | semidirect |
| 3. #26018261 | C2 | semidirect |
| 4. #26018176 | C2 | semidirect |
| 6. C2×#15667946 | C22 | semidirect |
| 10. C22⋊#13083549 | C22 | semidirect |
| 12. #19151361 | C22 | semidirect |
| 147. C89 | #12281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022435 | 2 |
| #26021680 | 2 |
| #26018261 | 2 |
| #26018176 | 2 |
| C89×#3186 | 2 |
| #12281 | 89 |