Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
362 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 2. #26022508 | C2 | semidirect |
| 3. #26022298 | C2 | semidirect |
| 4. #26019622 | C2 | semidirect |
| 5. #26018299 | C2 | semidirect |
| 6. #26018214 | C2 | semidirect |
| 7. C89×Q8⋊C16 | C2 | semidirect |
| 93. Q8×C89 | SD32 | semidirect |
| 147. Q8⋊C16 | D89 | semidirect |
| 149. C89 | #12332 | semidirect |
| 237. Q8 | #15667957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033227 | 2 |
| #26022508 | 2 |
| #26022298 | 2 |
| #26019622 | 2 |
| #26018299 | 2 |
| #26018214 | 2 |
| C89×Q8⋊C16 | 2 |
| #12332 | 89 |