Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #19151622 | C4 | semidirect |
| 8. C42×Dic89 | C4 | semidirect |
| 9. #19151393 | C4 | semidirect |
| 13. #354×C89 | C4 | semidirect |
| 124. C89 | #7500 | semidirect |
| 133. #354 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021917 | 2 |
| #26021081 | 2 |
| C89×#2126 | 2 |
| #7500 | 89 |