Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26022038 | C2 | semidirect |
| 4. #26021035 | C2 | semidirect |
| 5. #26018348 | C2 | semidirect |
| 6. #26018340 | C2 | semidirect |
| 20. #19151411 | C4 | semidirect |
| 36. #15667952 | C2×C4 | semidirect |
| 39. #15667948 | C2×C4 | semidirect |
| 167. C89 | #12940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029104 | 2 |
| #26022038 | 2 |
| C2×#19151411 | 2 |
| #26021035 | 2 |
| #26018348 | 2 |
| #26018340 | 2 |
| C2×#357×C89 | 2 |
| #12940 | 89 |