Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
326 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26018423 | C2 | semidirect |
| 8. C2×#125×C89 | C4 | semidirect |
| 9. #491×C89 | C4 | semidirect |
| 13. C4×M16×C89 | C4 | semidirect |
| 97. C89 | #13596 | semidirect |
| 99. C2×#125 | Dic89 | semidirect |
| 100. #491 | Dic89 | semidirect |
| 105. C4×M16 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021917 | 2 |
| #26018423 | 2 |
| C89×#3142 | 2 |
| #13596 | 89 |