Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1838 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1838 conjugacy classes of subgroups — too many to draw. Only its 219 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. C2×#19152233 | C2 | semidirect |
| 2. C2×#19151974 | C2 | semidirect |
| 3. C2×#19151794 | C2 | semidirect |
| 4. #26019307 | C2 | direct (N × H) |
| 5. C2×#19151325 | C2 | semidirect |
| 6. C2×#331×C89 | C2 | semidirect |
| 12. #19152233 | C22 | semidirect |
| 13. C2×#15668009 | C22 | semidirect |
| 18. #19151974 | C22 | semidirect |
| 20. #19151794 | C22 | semidirect |
| 22. C2×C4×#10623494 | C22 | semidirect |
| 23. #19151325 | C22 | semidirect |
| 25. C2×C4⋊C8×C89 | C22 | semidirect |
| 26. #331×C89 | C22 | semidirect |
| 44. #15668009 | C23 | semidirect |
| 58. C4×#10623494 | C23 | semidirect |
| 67. C4⋊C8×C89 | C23 | semidirect |
| 82. C2×D356 | D8 | semidirect |
| 154. D356 | C2×D8 | semidirect |
| 182. C2×C89 | #1619 | semidirect |
| 191. C2×#331 | D89 | semidirect |
| 193. C89 | C2×#1619 | semidirect |
| 209. C2×C4⋊C8 | C2×D89 | semidirect |
| 212. #331 | C2×D89 | semidirect |
| 251. C4⋊C8 | C22×D89 | semidirect |
| 370. C2 | #26019307 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152233 | 2 |
| C2×#19151974 | 2 |
| C2×#19151794 | 2 |
| #26019307 | 2 |
| C2×#19151325 | 2 |
| C2×#331×C89 | 2 |
| C2×#1619 | 89 |