Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
524 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 7. C2×#15667977 | C4 | semidirect |
| 10. #19151504 | C4 | semidirect |
| 13. #19151467 | C4 | semidirect |
| 15. #19151444 | C4 | semidirect |
| 53. C2×Dic178 | C4⋊C4 | semidirect |
| 75. C4×Dic89 | C4⋊C4 | semidirect |
| 168. C89 | #12800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022962 | 2 |
| C2×#19151392 | 2 |
| #26020238 | 2 |
| #26018377 | 2 |
| C89×#1393 | 2 |
| #12800 | 89 |