Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
450 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 61 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. #356×D89 | C2 | semidirect |
| 3. #26018419 | C2 | semidirect |
| 4. #26018418 | C2 | semidirect |
| 5. C89×#1410 | C2 | semidirect |
| 15. #19151397 | C22 | semidirect |
| 18. #356×C89 | C22 | semidirect |
| 134. D89 | #1410 | direct (N × H) |
| 139. #1410 | D89 | direct (N × H) |
| 140. C89 | C2×#1410 | semidirect |
| 153. #356 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #492×D89 | 2 |
| #356×D89 | 2 |
| #26018419 | 2 |
| #26018418 | 2 |
| C89×#1410 | 2 |
| C2×#1410 | 89 |