Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
240 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022401 | C2 | semidirect |
| 4. #26019058 | C2 | semidirect |
| 5. #26018315 | C2 | semidirect |
| 7. C89×#1365 | C2 | semidirect |
| 50. Dic356 | SD16 | semidirect |
| 114. #1365 | D89 | semidirect |
| 116. C89 | #12419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022401 | 2 |
| #26022293 | 2 |
| #26019845 | 2 |
| #26019058 | 2 |
| #26018315 | 2 |
| #26018297 | 2 |
| C89×#1365 | 2 |
| #12419 | 89 |