Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26021873 | C2 | semidirect |
| 3. #26018236 | C2 | semidirect |
| 4. C89×#1812 | C2 | semidirect |
| 5. C22×D712 | C4 | semidirect |
| 8. #19151851 | C4 | semidirect |
| 12. #19151636 | C4 | semidirect |
| 15. #19151380 | C22 | semidirect |
| 19. H(3,ℤ/4)×C89 | C22 | semidirect |
| 153. #1812 | D89 | semidirect |
| 155. C89 | #11868 | semidirect |
| 170. H(3,ℤ/4) | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029900 | 2 |
| #26021873 | 2 |
| #26018236 | 2 |
| C89×#1812 | 2 |
| #11868 | 89 |