Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26022475 | C2 | semidirect |
| 2. D4×#13083549 | C2 | semidirect |
| 3. #26019651 | C2 | semidirect |
| 4. #26018325 | C2 | semidirect |
| 5. #26018311 | C2 | semidirect |
| 6. #26018298 | C2 | semidirect |
| 119. C89 | #12468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022475 | 2 |
| D4×#13083549 | 2 |
| #26019651 | 2 |
| #26018325 | 2 |
| #26018311 | 2 |
| #26018298 | 2 |
| C89×#1667 | 2 |
| #12468 | 89 |