Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
906 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 211 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. #26030827 | C2 | semidirect |
| 2. #26030680 | C2 | semidirect |
| 3. #26019924 | C2 | semidirect |
| 4. #26019921 | C2 | semidirect |
| 5. #26019919 | C2 | semidirect |
| 6. #26019916 | C2 | semidirect |
| 7. C2×#19151319 | C2 | semidirect |
| 8. C89×#3147 | C2 | semidirect |
| 88. C2×C8×C89 | D8 | semidirect |
| 141. #3147 | D89 | semidirect |
| 147. C89 | #19616 | semidirect |
| 225. C2×C8 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030827 | 2 |
| #26030680 | 2 |
| #26019924 | 2 |
| #26019921 | 2 |
| #26019919 | 2 |
| #26019916 | 2 |
| C2×#19151319 | 2 |
| C89×#3147 | 2 |
| #19616 | 89 |