Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. #26022018 | C2 | semidirect |
| 4. #26020376 | C2 | semidirect |
| 5. #26018368 | C2 | semidirect |
| 6. #26018353 | C2 | semidirect |
| 19. #442×C89 | C4 | semidirect |
| 145. C89 | #12826 | semidirect |
| 150. #442 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022018 | 2 |
| C2×#19151411 | 2 |
| #26021968 | 2 |
| #26020376 | 2 |
| #26018368 | 2 |
| #26018353 | 2 |
| C89×#2948 | 2 |
| #12826 | 89 |