Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
338 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022430 | C2 | semidirect |
| 3. #26021692 | C2 | semidirect |
| 4. #26018267 | C2 | semidirect |
| 5. #26018267 | C2 | semidirect |
| 6. #26018178 | C2 | semidirect |
| 8. C2×#15667946 | C22 | semidirect |
| 14. C22⋊#13083549 | C22 | semidirect |
| 15. C22⋊#13083549 | C22 | semidirect |
| 17. #19151363 | C22 | semidirect |
| 171. C89 | #12284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022435 | 2 |
| #26022430 | 2 |
| #26021692 | 2 |
| #26018267 | 2 |
| #26018178 | 2 |
| C89×#3199 | 2 |
| #12284 | 89 |