Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26018763 | C2 | semidirect |
| 4. #26018145 | C2 | semidirect |
| 7. #19151957 | C4 | semidirect |
| 23. #15668012 | C2×C4 | semidirect |
| 33. #15667923 | C2×C4 | semidirect |
| 147. C89 | #9439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030638 | 2 |
| #26018876 | 2 |
| #26018763 | 2 |
| #26018145 | 2 |
| C89×#2372 | 2 |
| #9439 | 89 |