Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
770 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 1. #26028697 | C2 | semidirect |
| 3. #26018780 | C2 | semidirect |
| 4. #26018104 | C2 | semidirect |
| 5. C89×#1782 | C2 | semidirect |
| 7. C2×#15668008 | C4 | semidirect |
| 8. C2×#15668001 | C4 | semidirect |
| 15. #19151505 | C4 | semidirect |
| 16. #19151501 | C4 | semidirect |
| 49. C22⋊#10623494 | D4 | semidirect |
| 249. #1782 | D89 | semidirect |
| 252. C89 | #9445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028697 | 2 |
| #26023867 | 2 |
| #26018780 | 2 |
| #26018104 | 2 |
| C89×#1782 | 2 |
| #9445 | 89 |