Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 15. C4×#13083553 | C4 | semidirect |
| 16. C4×#13083553 | C4 | semidirect |
| 18. #19151444 | C4 | semidirect |
| 19. C42×Dic89 | C4 | semidirect |
| 206. C89 | #8740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022748 | 2 |
| #26020333 | 2 |
| #26020327 | 2 |
| #26018106 | 2 |
| #26018105 | 2 |
| #26018104 | 2 |
| C89×#1284 | 2 |
| #8740 | 89 |