Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
568 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26019983 | C2 | semidirect |
| 3. #26018563 | C2 | semidirect |
| 4. #26018250 | C2 | semidirect |
| 5. #26018249 | C2 | semidirect |
| 6. #26018248 | C2 | semidirect |
| 7. C89×#1343 | C2 | semidirect |
| 8. C2×#15668008 | C4 | semidirect |
| 13. #19151516 | C4 | semidirect |
| 15. #19151512 | C4 | semidirect |
| 19. #19151462 | C4 | semidirect |
| 242. #1343 | D89 | semidirect |
| 243. C89 | #11693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026001 | 2 |
| #26019983 | 2 |
| #26018563 | 2 |
| #26018250 | 2 |
| #26018249 | 2 |
| #26018248 | 2 |
| C89×#1343 | 2 |
| #11693 | 89 |