Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
338 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 21. #333×C89 | C4 | semidirect |
| 22. #332×C89 | C4 | semidirect |
| 146. C89 | #9579 | semidirect |
| 159. #333 | Dic89 | semidirect |
| 160. #332 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021230 | 2 |
| C4⋊C8×Dic89 | 2 |
| #26019023 | 2 |
| #26018655 | 2 |
| #26018149 | 2 |
| #26018084 | 2 |
| C89×#1542 | 2 |
| #9579 | 89 |