Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
532 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 532 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. #101×Dic89 | C2 | semidirect |
| 4. #26018378 | C2 | semidirect |
| 16. #19151395 | C4 | semidirect |
| 20. #355×C89 | C4 | semidirect |
| 38. #15667931 | C2×C4 | semidirect |
| 52. #101×C89 | C2×C4 | semidirect |
| 154. Dic89 | #355 | direct (N × H) |
| 167. C89 | C4×#355 | semidirect |
| 181. #355 | Dic89 | direct (N × H) |
| 210. #101 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #124×Dic89 | 2 |
| C2×#19151395 | 2 |
| #101×Dic89 | 2 |
| #26018378 | 2 |
| C2×#355×C89 | 2 |
| C4×#355 | 89 |