Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
592 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26018277 | C2 | semidirect |
| 4. #26018274 | C2 | semidirect |
| 6. C2×#15667991 | C4 | semidirect |
| 8. #19151534 | C4 | semidirect |
| 12. #19151510 | C4 | semidirect |
| 15. #19151458 | C4 | semidirect |
| 23. C22×Dic178 | C2×C4 | semidirect |
| 28. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 44. #15667919 | C2×C4 | semidirect |
| 45. #15667919 | C2×C4 | semidirect |
| 222. C89 | #11716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026057 | 2 |
| C2×#19151365 | 2 |
| #26018277 | 2 |
| #26018274 | 2 |
| C2×#323×C89 | 2 |
| #11716 | 89 |