Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26023332 | C2 | semidirect |
| 4. #26018825 | C2 | semidirect |
| 5. #26018131 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 9. #19151928 | C4 | semidirect |
| 12. #19151749 | C4 | semidirect |
| 104. C22⋊Dic89 | SD16 | semidirect |
| 251. C89 | #9278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031009 | 2 |
| #26023332 | 2 |
| #26021089 | 2 |
| #26018825 | 2 |
| #26018131 | 2 |
| #26018099 | 2 |
| C2×#327×C89 | 2 |
| #9278 | 89 |