Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2734 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 2734 conjugacy classes of subgroups — too many to draw. Only its 371 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 |
|---|---|---|
| 3. #26018495 | C2 | semidirect |
| 5. C22×#13083553 | C22 | semidirect |
| 9. #19151454 | C4 | semidirect |
| 10. C2×#15667919 | C22 | semidirect |
| 55. C24×C89 | C4⋊C4 | semidirect |
| 131. C89 | #14673 | semidirect |
| 173. C24 | #13083553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151454 | 2 |
| #26018495 | 2 |
| C2×#379×C89 | 2 |
| #14673 | 89 |