Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
406 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26032052 | C2 | semidirect |
| 2. #26022325 | C2 | semidirect |
| 3. #26019866 | C2 | semidirect |
| 4. #26018288 | C2 | semidirect |
| 5. #26018225 | C2 | semidirect |
| 6. #26018224 | C2 | semidirect |
| 7. C89×#2213 | C2 | semidirect |
| 17. #19151419 | C22 | semidirect |
| 19. C8×#10623494 | C22 | semidirect |
| 21. #493×C89 | C22 | semidirect |
| 23. #364×C89 | C22 | semidirect |
| 66. Dic356 | D8 | semidirect |
| 75. D712 | D8 | semidirect |
| 86. Q16×C89 | D8 | semidirect |
| 92. D8×C89 | D8 | semidirect |
| 151. #2213 | D89 | semidirect |
| 156. C89 | #12310 | semidirect |
| 163. #493 | C2×D89 | semidirect |
| 170. #364 | C2×D89 | semidirect |
| 219. Q16 | #13083559 | semidirect |
| 236. D8 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032052 | 2 |
| #26022325 | 2 |
| #26019866 | 2 |
| #26018288 | 2 |
| #26018225 | 2 |
| #26018224 | 2 |
| C89×#2213 | 2 |
| #12310 | 89 |