Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26022525 | C2 | semidirect |
| 5. #26018323 | C2 | semidirect |
| 6. #26018306 | C2 | semidirect |
| 7. C89×#1364 | C2 | semidirect |
| 58. #13083549 | SD16 | semidirect |
| 111. #1364 | D89 | semidirect |
| 112. C89 | #12451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022525 | 2 |
| #26022071 | 2 |
| #26019642 | 2 |
| #26019638 | 2 |
| #26018323 | 2 |
| #26018306 | 2 |
| C89×#1364 | 2 |
| #12451 | 89 |