Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1146 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1146 conjugacy classes of subgroups — too many to draw. Only its 251 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×#19151974 | C2 | semidirect |
| 2. C2×#19151971 | C2 | semidirect |
| 3. C2×#19151944 | C2 | semidirect |
| 4. #26019919 | C2 | direct (N × H) |
| 5. C2×#19151319 | C2 | semidirect |
| 6. C2×#493×C89 | C2 | semidirect |
| 12. #19151974 | C22 | semidirect |
| 14. #19151971 | C22 | semidirect |
| 16. #19151944 | C22 | semidirect |
| 19. #19151319 | C22 | semidirect |
| 23. #493×C89 | C22 | semidirect |
| 86. C2×C8×C89 | D8 | semidirect |
| 119. C8×C89 | C2×D8 | semidirect |
| 138. C2×C89 | #1721 | semidirect |
| 143. C2×#493 | D89 | semidirect |
| 148. C89 | C2×#1721 | semidirect |
| 158. #493 | C2×D89 | semidirect |
| 226. C2×C8 | #13083559 | semidirect |
| 262. C8 | C2×#13083559 | semidirect |
| 280. C2 | #26019919 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151974 | 2 |
| C2×#19151971 | 2 |
| C2×#19151944 | 2 |
| #26019919 | 2 |
| C2×#19151319 | 2 |
| C2×#493×C89 | 2 |
| C2×#1721 | 89 |