Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1250 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 183 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. #26030370 | C2 | semidirect |
| 2. #26023536 | C2 | semidirect |
| 3. #26019238 | C2 | semidirect |
| 4. #26019204 | C2 | semidirect |
| 5. #26018760 | C2 | semidirect |
| 6. #26018593 | C2 | semidirect |
| 8. C2×C4×Dic178 | C22 | semidirect |
| 9. #19151909 | C22 | semidirect |
| 12. #19151736 | C22 | semidirect |
| 14. #19151655 | C22 | semidirect |
| 16. #19151523 | C22 | semidirect |
| 18. #19151510 | C22 | semidirect |
| 20. #19151444 | C22 | semidirect |
| 21. #19151332 | C22 | semidirect |
| 22. #19151322 | C22 | semidirect |
| 210. C89 | #18179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030370 | 2 |
| #26023536 | 2 |
| #26019238 | 2 |
| #26019204 | 2 |
| #26018760 | 2 |
| #26018593 | 2 |
| C89×#3496 | 2 |
| #18179 | 89 |