Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1150 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1150 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×#19151993 | C2 | semidirect |
| 3. C2×#19151958 | C2 | semidirect |
| 4. #26019559 | C2 | direct (N × H) |
| 5. C2×#19151337 | C2 | semidirect |
| 6. C2×#329×C89 | C2 | semidirect |
| 12. C2×#15668012 | C22 | semidirect |
| 19. #19151993 | C22 | semidirect |
| 21. #19151958 | C22 | semidirect |
| 24. C2×#15667923 | C22 | semidirect |
| 25. #19151337 | C22 | semidirect |
| 27. C2×#97×C89 | C22 | semidirect |
| 28. #329×C89 | C22 | semidirect |
| 42. #15668012 | C23 | semidirect |
| 64. #15667923 | C23 | semidirect |
| 74. #97×C89 | C23 | semidirect |
| 183. C2×C89 | #1659 | semidirect |
| 192. C2×#329 | D89 | semidirect |
| 193. C89 | C2×#1659 | semidirect |
| 213. C2×#97 | C2×D89 | semidirect |
| 215. #329 | C2×D89 | semidirect |
| 261. #97 | C22×D89 | semidirect |
| 370. C2 | #26019559 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152340 | 2 |
| C2×#19151993 | 2 |
| C2×#19151958 | 2 |
| #26019559 | 2 |
| C2×#19151337 | 2 |
| C2×#329×C89 | 2 |
| C2×#1659 | 89 |