Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 3. C4×#15667945 | C2 | semidirect |
| 4. #26018751 | C2 | semidirect |
| 6. #26018539 | C2 | semidirect |
| 7. C89×#1986 | C2 | semidirect |
| 9. #19151994 | C4 | semidirect |
| 10. #19151972 | C4 | semidirect |
| 11. #19151948 | C4 | semidirect |
| 12. #19151946 | C4 | semidirect |
| 163. #10623494 | #104 | semidirect |
| 192. #1986 | D89 | semidirect |
| 198. C89 | #9722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030812 | 2 |
| #26021171 | 2 |
| C4×#15667945 | 2 |
| #26018751 | 2 |
| #26018746 | 2 |
| #26018539 | 2 |
| C89×#1986 | 2 |
| #9722 | 89 |