Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#19151421 | C2 | semidirect |
| 4. #26021006 | C2 | semidirect |
| 5. #26018357 | C2 | semidirect |
| 6. #26018331 | C2 | semidirect |
| 23. #357×C89 | C4 | semidirect |
| 54. C2×C16×C89 | C2×C4 | semidirect |
| 55. #107×C89 | C2×C4 | semidirect |
| 152. C89 | #12956 | semidirect |
| 167. #357 | Dic89 | semidirect |
| 191. C2×C16 | C2×Dic89 | semidirect |
| 194. #107 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151710 | 2 |
| C2×#19151421 | 2 |
| C2×#19151411 | 2 |
| #26021006 | 2 |
| #26018357 | 2 |
| #26018331 | 2 |
| C89×#2140 | 2 |
| #12956 | 89 |