Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
510 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26020030 | C2 | semidirect |
| 4. #26018139 | C2 | semidirect |
| 5. C89×#1297 | C2 | semidirect |
| 6. C2×#15668020 | C4 | semidirect |
| 11. #19151626 | C4 | semidirect |
| 12. #19151566 | C4 | semidirect |
| 14. #19151556 | C4 | semidirect |
| 17. #19151334 | C4 | semidirect |
| 18. #19151331 | C4 | semidirect |
| 148. #1297 | D89 | semidirect |
| 149. C89 | #8239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028942 | 2 |
| #26020030 | 2 |
| #26018741 | 2 |
| #26018139 | 2 |
| C89×#1297 | 2 |
| #8239 | 89 |