Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
778 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 143 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. #26032064 | C2 | semidirect |
| 2. #26031851 | C2 | semidirect |
| 3. #26019714 | C2 | semidirect |
| 4. #26019686 | C2 | semidirect |
| 5. #26019484 | C2 | semidirect |
| 6. #26019304 | C2 | semidirect |
| 7. #26019138 | C2 | semidirect |
| 8. C8×D712 | C2 | semidirect |
| 9. C89×#1706 | C2 | semidirect |
| 12. #19152233 | C22 | semidirect |
| 14. #19151875 | C22 | semidirect |
| 17. #19151800 | C22 | semidirect |
| 25. #19151677 | C22 | semidirect |
| 26. C8×D356 | C22 | semidirect |
| 28. #19151351 | C22 | semidirect |
| 29. #19151351 | C22 | semidirect |
| 30. #19151344 | C22 | semidirect |
| 31. #19151342 | C22 | semidirect |
| 32. #19151327 | C22 | semidirect |
| 33. #19151327 | C22 | semidirect |
| 34. #500×C89 | C22 | semidirect |
| 36. #492×C89 | C22 | semidirect |
| 37. #486×C89 | C22 | semidirect |
| 38. C82×C89 | C22 | semidirect |
| 100. D712 | D8 | semidirect |
| 195. #1706 | D89 | semidirect |
| 202. C89 | #19884 | semidirect |
| 206. #500 | C2×D89 | semidirect |
| 208. #492 | C2×D89 | semidirect |
| 209. #486 | C2×D89 | semidirect |
| 231. C82 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032064 | 2 |
| #26031851 | 2 |
| #26019714 | 2 |
| #26019686 | 2 |
| #26019484 | 2 |
| #26019304 | 2 |
| #26019138 | 2 |
| C8×D712 | 2 |
| C89×#1706 | 2 |
| #19884 | 89 |