Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
200 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 200 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 |
|---|---|---|
| 3. #26018451 | C2 | semidirect |
| 4. #26018433 | C2 | semidirect |
| 6. #26018386 | C2 | semidirect |
| 7. C4×Q32×C89 | C2 | semidirect |
| 10. #19151435 | C4 | semidirect |
| 27. #15667918 | C2×C4 | semidirect |
| 31. Q32×C89 | C2×C4 | semidirect |
| 87. C4×Q32 | D89 | semidirect |
| 93. C89 | #13652 | semidirect |
| 111. Q32 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151435 | 2 |
| C4×D1424 | 2 |
| #26018451 | 2 |
| #26018433 | 2 |
| #26018429 | 2 |
| #26018386 | 2 |
| C4×Q32×C89 | 2 |
| #13652 | 89 |