Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
384 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 384 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. #26022519 | C2 | semidirect |
| 2. #26022292 | C2 | semidirect |
| 3. #26019731 | C2 | semidirect |
| 4. #26018295 | C2 | semidirect |
| 5. #26018222 | C2 | semidirect |
| 6. #26018210 | C2 | semidirect |
| 7. C89×#3277 | C2 | semidirect |
| 93. Q16×C89 | D8 | semidirect |
| 173. #3277 | D89 | semidirect |
| 180. C89 | #12325 | semidirect |
| 258. Q16 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022519 | 2 |
| #26022292 | 2 |
| #26019731 | 2 |
| #26018295 | 2 |
| #26018222 | 2 |
| #26018210 | 2 |
| C89×#3277 | 2 |
| #12325 | 89 |