Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 123 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. C4×#15667931 | C2 | semidirect |
| 4. #26018378 | C2 | semidirect |
| 5. C4×#101×C89 | C2 | semidirect |
| 18. #19151394 | C4 | semidirect |
| 42. #15667931 | C2×C4 | semidirect |
| 60. #101×C89 | C2×C4 | semidirect |
| 189. C4×#101 | D89 | semidirect |
| 191. C89 | #12632 | semidirect |
| 240. #101 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022959 | 2 |
| C2×#19151394 | 2 |
| C4×#15667931 | 2 |
| #26018378 | 2 |
| C4×#101×C89 | 2 |
| #12632 | 89 |