Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1074 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 203 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×#19151977 | C2 | semidirect |
| 3. C2×#19151889 | C2 | semidirect |
| 4. #26019398 | C2 | direct (N × H) |
| 5. C2×#19151325 | C2 | semidirect |
| 6. C2×#333×C89 | C2 | semidirect |
| 17. #19151977 | C22 | semidirect |
| 19. #19151889 | C22 | semidirect |
| 23. #19151325 | C22 | semidirect |
| 26. #333×C89 | C22 | semidirect |
| 152. C2×C89 | #1634 | semidirect |
| 160. C2×#333 | D89 | semidirect |
| 162. C89 | C2×#1634 | semidirect |
| 181. #333 | C2×D89 | semidirect |
| 308. C2 | #26019398 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152314 | 2 |
| C2×#19151977 | 2 |
| C2×#19151889 | 2 |
| #26019398 | 2 |
| C2×#19151325 | 2 |
| C2×#333×C89 | 2 |
| C2×#1634 | 89 |