Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1182 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 1182 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 |
|---|---|---|
| 9. #19151466 | C4 | semidirect |
| 50. C42×C89 | C4⋊C4 | semidirect |
| 95. C89 | #14678 | semidirect |
| 140. C42 | #13083553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151468 | 2 |
| C2×#19151466 | 2 |
| #26018516 | 2 |
| #26018508 | 2 |
| C2×#383×C89 | 2 |
| #14678 | 89 |