Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
720 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 720 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. #99×Dic89 | C2 | semidirect |
| 4. #26018376 | C2 | semidirect |
| 7. C2×D4×Dic89 | C4 | semidirect |
| 11. #19151501 | C4 | semidirect |
| 13. #19151468 | C4 | semidirect |
| 15. C42×Dic89 | C4 | semidirect |
| 16. #19151391 | C4 | semidirect |
| 20. #353×C89 | C4 | semidirect |
| 42. #15667927 | C2×C4 | semidirect |
| 53. #99×C89 | C2×C4 | semidirect |
| 92. C2×D4×C89 | C42 | semidirect |
| 102. C42×C89 | C42 | semidirect |
| 178. Dic89 | #353 | direct (N × H) |
| 193. C89 | C4×#353 | semidirect |
| 207. #353 | Dic89 | direct (N × H) |
| 240. #99 | C2×Dic89 | semidirect |
| 253. C2×D4 | C4×Dic89 | semidirect |
| 290. C42 | C4×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×Dic89 | 2 |
| C2×#19151391 | 2 |
| #99×Dic89 | 2 |
| #26018376 | 2 |
| C2×#353×C89 | 2 |
| C4×#353 | 89 |