Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
3294 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 627 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. #26028517 | C2 | direct (N × H) |
| 2. C2×#19151534 | C2 | semidirect |
| 3. C2×#19151522 | C2 | semidirect |
| 4. C2×#19151520 | C2 | semidirect |
| 6. C2×#399×C89 | C2 | semidirect |
| 8. C22×C4⋊Dic89 | C22 | semidirect |
| 9. C22×#13083553 | C22 | semidirect |
| 13. #19151534 | C22 | semidirect |
| 14. #19151522 | C22 | semidirect |
| 15. #19151520 | C22 | semidirect |
| 17. C2×#15667919 | C22 | semidirect |
| 18. C22×C4⋊C4×C89 | C22 | semidirect |
| 20. #399×C89 | C22 | semidirect |
| 21. C2×#95×C89 | C22 | semidirect |
| 29. C2×C4⋊Dic89 | C23 | semidirect |
| 31. C2×#13083553 | C23 | semidirect |
| 38. #15667919 | C23 | semidirect |
| 43. C2×C4⋊C4×C89 | C23 | semidirect |
| 46. #95×C89 | C23 | semidirect |
| 129. C2×C89 | #2842 | semidirect |
| 136. C2×#399 | D89 | semidirect |
| 140. C89 | C2×#2842 | semidirect |
| 144. C22×C4⋊C4 | C2×D89 | semidirect |
| 150. #399 | C2×D89 | semidirect |
| 155. C2×#95 | C2×D89 | semidirect |
| 170. C2×C4⋊C4 | C22×D89 | semidirect |
| 180. #95 | C22×D89 | semidirect |
| 263. C2 | #26028517 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028517 | 2 |
| C2×#19151534 | 2 |
| C2×#19151522 | 2 |
| C2×#19151520 | 2 |
| C2×#19151453 | 2 |
| C2×#399×C89 | 2 |
| C2×#2842 | 89 |