Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1190 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1190 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 |
|---|---|---|
| 1. C2×#19152314 | C2 | semidirect |
| 2. C2×#19151790 | C2 | semidirect |
| 3. #26019333 | C2 | direct (N × H) |
| 4. C2×#19151347 | C2 | semidirect |
| 5. C2×#19151327 | C2 | semidirect |
| 6. C2×#492×C89 | C2 | semidirect |
| 10. #19152314 | C22 | semidirect |
| 16. #19151790 | C22 | semidirect |
| 19. #19151347 | C22 | semidirect |
| 20. #19151327 | C22 | semidirect |
| 25. #492×C89 | C22 | semidirect |
| 163. C2×C89 | #1624 | semidirect |
| 168. C2×#492 | D89 | semidirect |
| 173. C89 | C2×#1624 | semidirect |
| 186. #492 | C2×D89 | semidirect |
| 330. C2 | #26019333 | 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×#19151790 | 2 |
| #26019333 | 2 |
| C2×#19151347 | 2 |
| C2×#19151327 | 2 |
| C2×#492×C89 | 2 |
| C2×#1624 | 89 |