Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
648 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4×#15667927 | C2 | semidirect |
| 3. #26018274 | C2 | semidirect |
| 4. #26018250 | C2 | semidirect |
| 5. C89×#1460 | C2 | semidirect |
| 6. C22×#13083574 | C4 | semidirect |
| 9. #19151518 | C4 | semidirect |
| 10. #19151515 | C4 | semidirect |
| 17. C4×C22⋊Dic89 | C4 | semidirect |
| 213. #1460 | D89 | semidirect |
| 216. C89 | #11725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023467 | 2 |
| C4×#15667927 | 2 |
| #26018274 | 2 |
| #26018250 | 2 |
| C89×#1460 | 2 |
| #11725 | 89 |