Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
722 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#19151387 | C2 | semidirect |
| 4. #26018369 | C2 | semidirect |
| 7. C2×#15667993 | C4 | semidirect |
| 9. C22×#13083553 | C4 | semidirect |
| 15. #19151478 | C4 | semidirect |
| 19. #19151461 | C4 | semidirect |
| 247. C89 | #13081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151582 | 2 |
| #26023583 | 2 |
| C2×#19151387 | 2 |
| #26018369 | 2 |
| C89×#1782 | 2 |
| #13081 | 89 |