Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
608 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 165 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. #26033227 | C2 | semidirect |
| 2. #26022501 | C2 | semidirect |
| 3. #26022287 | C2 | semidirect |
| 4. #26022284 | C2 | semidirect |
| 5. Q8×#13083549 | C2 | semidirect |
| 6. C4×#15667953 | C2 | semidirect |
| 7. C89×#3391 | C2 | semidirect |
| 58. #13083549 | #41 | semidirect |
| 76. Q8×C89 | D16 | semidirect |
| 115. #3391 | D89 | semidirect |
| 121. C89 | #33958 | semidirect |
| 190. Q8 | #15667953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033227 | 2 |
| #26022501 | 2 |
| #26022287 | 2 |
| #26022284 | 2 |
| Q8×#13083549 | 2 |
| C4×#15667953 | 2 |
| C89×#3391 | 2 |
| #33958 | 89 |