Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
450 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 450 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 |
|---|---|---|
| 4. #26018847 | C2 | semidirect |
| 5. #26018145 | C2 | semidirect |
| 6. #26018125 | C2 | semidirect |
| 7. C89×#1506 | C2 | semidirect |
| 10. #19151890 | C4 | semidirect |
| 11. #19151885 | C4 | semidirect |
| 12. #19151805 | C4 | semidirect |
| 13. #19151800 | C4 | semidirect |
| 199. #1506 | D89 | semidirect |
| 202. C89 | #9160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030408 | 2 |
| #26029269 | 2 |
| #26020063 | 2 |
| #26018847 | 2 |
| #26018145 | 2 |
| #26018125 | 2 |
| C89×#1506 | 2 |
| #9160 | 89 |