Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
322 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. #26018301 | C2 | semidirect |
| 5. Q8⋊#13083549 | C2 | semidirect |
| 6. #26018216 | C2 | semidirect |
| 7. C89×#3395 | C2 | semidirect |
| 95. Q8×C89 | SD32 | semidirect |
| 133. #3395 | D89 | semidirect |
| 140. C89 | #12330 | semidirect |
| 228. Q8 | #15667955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022509 | 2 |
| #26022292 | 2 |
| #26019612 | 2 |
| #26018301 | 2 |
| Q8⋊#13083549 | 2 |
| #26018216 | 2 |
| C89×#3395 | 2 |
| #12330 | 89 |