Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
406 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #26022026 | C2 | semidirect |
| 4. #26020998 | C2 | semidirect |
| 5. #26018354 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 19. #19151408 | C4 | semidirect |
| 36. #15667952 | C2×C4 | semidirect |
| 40. #15667944 | C2×C4 | semidirect |
| 162. C89 | #12951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×Dic89 | 2 |
| #26022026 | 2 |
| #26021988 | 2 |
| #26020998 | 2 |
| #26018354 | 2 |
| #26018333 | 2 |
| C89×#2148 | 2 |
| #12951 | 89 |