Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #26022063 | C2 | semidirect |
| 3. #26018556 | C2 | semidirect |
| 4. #26018229 | C2 | semidirect |
| 5. #26018225 | C2 | semidirect |
| 6. #26018224 | C2 | semidirect |
| 7. C89×#1336 | C2 | semidirect |
| 19. #19151419 | C22 | semidirect |
| 23. C8×#10623494 | C22 | semidirect |
| 25. #364×C89 | C22 | semidirect |
| 26. #322×C89 | C22 | semidirect |
| 75. Dic356 | M16 | semidirect |
| 80. D712 | M16 | semidirect |
| 103. Q16×C89 | M16 | semidirect |
| 105. D8×C89 | M16 | semidirect |
| 171. #1336 | D89 | semidirect |
| 174. C89 | #11669 | semidirect |
| 188. #364 | C2×D89 | semidirect |
| 192. #322 | C2×D89 | semidirect |
| 245. Q16 | #13083557 | semidirect |
| 252. D8 | #13083557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029157 | 2 |
| #26022063 | 2 |
| #26018556 | 2 |
| #26018229 | 2 |
| #26018225 | 2 |
| #26018224 | 2 |
| C89×#1336 | 2 |
| #11669 | 89 |