Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
454 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26021917 | C2 | semidirect |
| 3. #26018410 | C2 | semidirect |
| 4. C89×#2132 | C2 | semidirect |
| 7. C2×#15668009 | C4 | semidirect |
| 8. #19151988 | C4 | semidirect |
| 13. C4×#13083558 | C4 | semidirect |
| 14. #19151393 | C22 | semidirect |
| 19. #355×C89 | C22 | semidirect |
| 158. #2132 | D89 | semidirect |
| 161. C89 | #13579 | semidirect |
| 174. #355 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030705 | 2 |
| #26021917 | 2 |
| #26018410 | 2 |
| C89×#2132 | 2 |
| #13579 | 89 |