Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19152016 | C2 | semidirect |
| 3. #26021989 | C2 | semidirect |
| 4. C2×#19151404 | C2 | semidirect |
| 5. #26020307 | C2 | semidirect |
| 6. #26018349 | C2 | semidirect |
| 7. C89×#1388 | C2 | semidirect |
| 16. #19151874 | C4 | semidirect |
| 17. #19151869 | C4 | semidirect |
| 186. #1388 | D89 | semidirect |
| 188. C89 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152016 | 2 |
| #26029973 | 2 |
| #26021989 | 2 |
| C2×#19151404 | 2 |
| #26020307 | 2 |
| #26018349 | 2 |
| C89×#1388 | 2 |
| #13071 | 89 |