Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
468 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26022527 | C2 | semidirect |
| 3. #26022459 | C2 | semidirect |
| 4. #26022394 | C2 | semidirect |
| 5. #26022340 | C2 | semidirect |
| 7. #26022033 | C2 | semidirect |
| 8. C4×Q32×C89 | C2 | semidirect |
| 118. C4×Q32 | D89 | semidirect |
| 121. C89 | #33909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032684 | 2 |
| #26022527 | 2 |
| #26022459 | 2 |
| #26022394 | 2 |
| #26022340 | 2 |
| C16×D356 | 2 |
| #26022033 | 2 |
| C4×Q32×C89 | 2 |
| #33909 | 89 |