Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×D1424 | C2 | semidirect |
| 2. C2×#19152014 | C2 | semidirect |
| 3. #26029901 | C2 | semidirect |
| 4. #26022356 | C2 | semidirect |
| 5. #26022339 | C2 | semidirect |
| 6. #26021967 | C2 | semidirect |
| 7. C89×#2158 | C2 | semidirect |
| 16. C2×#15667951 | C22 | semidirect |
| 17. C2×C16×D89 | C22 | semidirect |
| 19. #19151835 | C22 | semidirect |
| 21. #19151398 | C22 | semidirect |
| 24. #367×C89 | C22 | semidirect |
| 25. #366×C89 | C22 | semidirect |
| 50. C2×C16×C89 | D4 | semidirect |
| 135. #2158 | D89 | semidirect |
| 137. C89 | #33607 | semidirect |
| 153. #367 | C2×D89 | semidirect |
| 154. #366 | C2×D89 | semidirect |
| 179. C2×C16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1424 | 2 |
| C2×#19152014 | 2 |
| #26029901 | 2 |
| #26022356 | 2 |
| #26022339 | 2 |
| #26021967 | 2 |
| C89×#2158 | 2 |
| #33607 | 89 |