Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
958 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 958 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 |
|---|---|---|
| 2. C2×#19151960 | C2 | semidirect |
| 3. #26019573 | C2 | direct (N × H) |
| 4. C2×#19151340 | C2 | semidirect |
| 5. C2×#19151337 | C2 | semidirect |
| 6. C2×#491×C89 | C2 | semidirect |
| 15. #19151960 | C22 | semidirect |
| 19. #19151340 | C22 | semidirect |
| 20. #19151337 | C22 | semidirect |
| 24. #491×C89 | C22 | semidirect |
| 145. C2×C89 | #1662 | semidirect |
| 150. C2×#491 | D89 | semidirect |
| 155. C89 | C2×#1662 | semidirect |
| 166. #491 | C2×D89 | semidirect |
| 294. C2 | #26019573 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152346 | 2 |
| C2×#19151960 | 2 |
| #26019573 | 2 |
| C2×#19151340 | 2 |
| C2×#19151337 | 2 |
| C2×#491×C89 | 2 |
| C2×#1662 | 89 |