Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
566 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26023131 | C2 | semidirect |
| 4. #26020340 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 7. C89×#1289 | C2 | semidirect |
| 13. C2×#15667944 | C4 | semidirect |
| 14. C2×#15667934 | C4 | semidirect |
| 229. #1289 | D89 | semidirect |
| 231. C89 | #9261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151917 | 2 |
| #26023131 | 2 |
| #26021087 | 2 |
| #26020340 | 2 |
| #26018819 | 2 |
| #26018099 | 2 |
| C89×#1289 | 2 |
| #9261 | 89 |