Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
268 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 268 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. #26022501 | C2 | semidirect |
| 2. D4×#13083549 | C2 | semidirect |
| 3. #26019607 | C2 | semidirect |
| 4. #26018323 | C2 | semidirect |
| 5. #26018298 | C2 | semidirect |
| 6. #26018297 | C2 | semidirect |
| 7. C89×#1667 | C2 | semidirect |
| 56. #13083549 | D8 | semidirect |
| 84. D4×C89 | D16 | semidirect |
| 128. #1667 | D89 | semidirect |
| 132. C89 | #12430 | semidirect |
| 214. D4 | #15667953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022501 | 2 |
| D4×#13083549 | 2 |
| #26019607 | 2 |
| #26018323 | 2 |
| #26018298 | 2 |
| #26018297 | 2 |
| C89×#1667 | 2 |
| #12430 | 89 |