Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1386 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1386 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. #26030339 | C2 | semidirect |
| 2. #26023531 | C2 | semidirect |
| 3. #26019272 | C2 | semidirect |
| 4. #26019170 | C2 | semidirect |
| 5. #26018760 | C2 | semidirect |
| 6. #26018593 | C2 | semidirect |
| 7. C89×#3496 | C2 | semidirect |
| 8. C2×C4×D356 | C22 | semidirect |
| 10. #19151914 | C22 | semidirect |
| 13. #19151731 | C22 | semidirect |
| 15. #19151655 | C22 | semidirect |
| 16. #19151534 | C22 | semidirect |
| 18. #19151507 | C22 | semidirect |
| 20. #19151444 | C22 | semidirect |
| 21. #19151332 | C22 | semidirect |
| 22. #19151322 | C22 | semidirect |
| 61. C4⋊Q8×C89 | D4 | semidirect |
| 62. #127×C89 | D4 | semidirect |
| 76. C4×D4×C89 | D4 | semidirect |
| 219. #3496 | D89 | semidirect |
| 226. C89 | #18178 | semidirect |
| 263. C4⋊Q8 | C22⋊D89 | semidirect |
| 264. #127 | C22⋊D89 | semidirect |
| 281. C4×D4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030339 | 2 |
| #26023531 | 2 |
| #26019272 | 2 |
| #26019170 | 2 |
| #26018760 | 2 |
| #26018593 | 2 |
| C89×#3496 | 2 |
| #18178 | 89 |