Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
726 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. #26022838 | C2 | semidirect |
| 2. #26020176 | C2 | semidirect |
| 4. #26018105 | C2 | semidirect |
| 14. C2×#124×C89 | C4 | semidirect |
| 17. #391×C89 | C4 | semidirect |
| 173. C89 | #9466 | semidirect |
| 175. C2×#124 | Dic89 | semidirect |
| 182. #391 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022838 | 2 |
| #26020176 | 2 |
| #26018781 | 2 |
| #26018105 | 2 |
| C89×#2436 | 2 |
| #9466 | 89 |