Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
474 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26029264 | C2 | semidirect |
| 3. #26020065 | C2 | semidirect |
| 4. #26018843 | C2 | semidirect |
| 5. #26018761 | C2 | semidirect |
| 6. #26018144 | C2 | semidirect |
| 7. C89×#1291 | C2 | semidirect |
| 11. #19151884 | C4 | semidirect |
| 12. #19151879 | C4 | semidirect |
| 13. #19151799 | C4 | semidirect |
| 14. #19151794 | C4 | semidirect |
| 209. #1291 | D89 | semidirect |
| 210. C89 | #9161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030404 | 2 |
| #26029264 | 2 |
| #26020065 | 2 |
| #26018843 | 2 |
| #26018761 | 2 |
| #26018144 | 2 |
| C89×#1291 | 2 |
| #9161 | 89 |