Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#19151375 | C2 | semidirect |
| 5. #26020160 | C2 | semidirect |
| 6. #26018355 | C2 | semidirect |
| 7. C89×#1388 | C2 | semidirect |
| 17. #19151415 | C4 | semidirect |
| 18. #19151412 | C4 | semidirect |
| 19. #19151404 | C4 | semidirect |
| 150. #1388 | D89 | semidirect |
| 152. C89 | #12651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151719 | 2 |
| #26022002 | 2 |
| #26021979 | 2 |
| C2×#19151375 | 2 |
| #26020160 | 2 |
| #26018355 | 2 |
| C89×#1388 | 2 |
| #12651 | 89 |