Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1030 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1030 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 |
|---|---|---|
| 2. C2×#19151972 | C2 | semidirect |
| 3. C2×#19151946 | C2 | semidirect |
| 4. #26019881 | C2 | direct (N × H) |
| 5. C2×#19151319 | C2 | semidirect |
| 6. C2×#498×C89 | C2 | semidirect |
| 14. #19151972 | C22 | semidirect |
| 16. #19151946 | C22 | semidirect |
| 19. #19151319 | C22 | semidirect |
| 22. #498×C89 | C22 | semidirect |
| 79. C2×C8×C89 | SD16 | semidirect |
| 113. C8×C89 | C2×SD16 | semidirect |
| 130. C2×C89 | #1715 | semidirect |
| 135. C2×#498 | D89 | semidirect |
| 141. C89 | C2×#1715 | semidirect |
| 148. #498 | C2×D89 | semidirect |
| 214. C2×C8 | #13083561 | semidirect |
| 249. C8 | C2×#13083561 | semidirect |
| 266. C2 | #26019881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151975 | 2 |
| C2×#19151972 | 2 |
| C2×#19151946 | 2 |
| #26019881 | 2 |
| C2×#19151319 | 2 |
| C2×#498×C89 | 2 |
| C2×#1715 | 89 |