Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
768 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 768 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 |
|---|---|---|
| 2. #26020721 | C2 | semidirect |
| 3. #26020683 | C2 | semidirect |
| 6. #26018771 | C2 | semidirect |
| 7. C89×#1996 | C2 | semidirect |
| 15. #19152229 | C4 | semidirect |
| 19. #19152195 | C4 | semidirect |
| 297. #1996 | D89 | semidirect |
| 303. C89 | #8482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034497 | 2 |
| #26020721 | 2 |
| #26020683 | 2 |
| #26020552 | 2 |
| #26018793 | 2 |
| #26018771 | 2 |
| C89×#1996 | 2 |
| #8482 | 89 |