Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
268 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 268 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. #26022501 | C2 | semidirect |
| 2. #26022071 | C2 | semidirect |
| 3. #26019608 | C2 | semidirect |
| 4. #26019604 | C2 | semidirect |
| 5. #26018323 | C2 | semidirect |
| 6. #26018299 | C2 | semidirect |
| 7. C89×#1361 | C2 | semidirect |
| 63. #13083549 | D8 | semidirect |
| 93. D356 | D16 | semidirect |
| 131. #1361 | D89 | semidirect |
| 132. C89 | #12430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022501 | 2 |
| #26022071 | 2 |
| #26019608 | 2 |
| #26019604 | 2 |
| #26018323 | 2 |
| #26018299 | 2 |
| C89×#1361 | 2 |
| #12430 | 89 |