Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 388 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 |
| 7. #533×C89 | C4 | semidirect |
| 9. #490×C89 | C4 | semidirect |
| 13. C4×M16×C89 | C4 | semidirect |
| 25. #125×C89 | C2×C4 | semidirect |
| 32. #97×C89 | C2×C4 | semidirect |
| 107. C89 | #13595 | semidirect |
| 108. #533 | Dic89 | semidirect |
| 110. #490 | Dic89 | semidirect |
| 115. C4×M16 | Dic89 | semidirect |
| 126. #125 | C2×Dic89 | semidirect |
| 136. #97 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151391 | 2 |
| #26018423 | 2 |
| C89×#3138 | 2 |
| #13595 | 89 |