Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
840 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 840 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. #26022605 | C2 | semidirect |
| 3. #26018769 | C2 | semidirect |
| 4. #26018137 | C2 | semidirect |
| 5. C89×#1462 | C2 | semidirect |
| 10. #19151534 | C4 | semidirect |
| 11. #19151507 | C4 | semidirect |
| 21. C22×D356 | C2×C4 | semidirect |
| 29. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 42. #15667919 | C2×C4 | semidirect |
| 43. #15667919 | D4 | semidirect |
| 192. #1462 | D89 | semidirect |
| 194. C89 | #9409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025183 | 2 |
| #26022605 | 2 |
| #26018769 | 2 |
| #26018137 | 2 |
| C89×#1462 | 2 |
| #9409 | 89 |