Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26018413 | C2 | semidirect |
| 5. #26018412 | C2 | semidirect |
| 6. #26018411 | C2 | semidirect |
| 7. C89×#1407 | C2 | semidirect |
| 11. C4⋊Q8×D89 | C4 | semidirect |
| 13. #19151992 | C4 | semidirect |
| 14. #19151990 | C4 | semidirect |
| 19. #19151550 | C4 | semidirect |
| 187. #1407 | D89 | semidirect |
| 188. C89 | #13580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030708 | 2 |
| #26021934 | 2 |
| #26021916 | 2 |
| #26018413 | 2 |
| #26018412 | 2 |
| #26018411 | 2 |
| C89×#1407 | 2 |
| #13580 | 89 |