Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
356 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 2. #26018182 | C2 | semidirect |
| 3. C89×#1317 | C2 | semidirect |
| 15. C22×Dic178 | C8 | semidirect |
| 16. C22×D356 | C8 | semidirect |
| 134. #1317 | D89 | semidirect |
| 135. C89 | #7339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020169 | 2 |
| #26018182 | 2 |
| C89×#1317 | 2 |
| #7339 | 89 |