Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
480 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 480 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. #26023000 | C2 | semidirect |
| 4. #26018936 | C2 | semidirect |
| 6. #26018111 | C2 | semidirect |
| 7. C89×#1274 | C2 | semidirect |
| 10. #19151996 | C4 | semidirect |
| 11. #19151945 | C4 | semidirect |
| 188. #1274 | D89 | semidirect |
| 189. C89 | #9302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031382 | 2 |
| #26023000 | 2 |
| #26021084 | 2 |
| #26018936 | 2 |
| #26018813 | 2 |
| #26018111 | 2 |
| C89×#1274 | 2 |
| #9302 | 89 |