Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
684 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. #26018825 | C2 | semidirect |
| 4. #26018120 | C2 | semidirect |
| 8. #19151534 | C4 | semidirect |
| 10. #19151510 | C4 | semidirect |
| 21. C22×Dic178 | C2×C4 | semidirect |
| 28. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 41. #15667919 | C2×C4 | semidirect |
| 198. C89 | #9199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026057 | 2 |
| #26022866 | 2 |
| #26018825 | 2 |
| #26018120 | 2 |
| C2×#323×C89 | 2 |
| #9199 | 89 |