Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
846 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26020352 | C2 | semidirect |
| 3. #26018767 | C2 | semidirect |
| 4. #26018590 | C2 | semidirect |
| 5. C4×#99×C89 | C2 | semidirect |
| 8. C2×#15668012 | C4 | semidirect |
| 11. C2×#15667986 | C4 | semidirect |
| 14. C2×C4×D356 | C4 | semidirect |
| 15. C2×#15667971 | C4 | semidirect |
| 223. C4×#99 | D89 | semidirect |
| 226. C89 | #8360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152313 | 2 |
| #26020352 | 2 |
| #26018767 | 2 |
| #26018590 | 2 |
| C4×#99×C89 | 2 |
| #8360 | 89 |