Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 147 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×#19151381 | C2 | semidirect |
| 3. #26021863 | C2 | semidirect |
| 4. #26018340 | C2 | semidirect |
| 5. C23×C16×C89 | C2 | semidirect |
| 52. C2×C16×C89 | D4 | semidirect |
| 123. C22×C89 | #350 | semidirect |
| 140. C23×C16 | D89 | semidirect |
| 145. C89 | #12983 | semidirect |
| 187. C2×C16 | C22⋊D89 | semidirect |
| 265. C22 | #19151381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028946 | 2 |
| C2×#19151381 | 2 |
| #26021863 | 2 |
| #26018340 | 2 |
| C23×C16×C89 | 2 |
| #12983 | 89 |