Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 12. #19151320 | C4 | semidirect |
| 13. #19151320 | C4 | semidirect |
| 14. #19151319 | C4 | semidirect |
| 15. C8×#10623494 | C4 | semidirect |
| 109. C89 | #8804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018555 | 2 |
| #26018125 | 2 |
| #26018124 | 2 |
| #26018123 | 2 |
| #26018116 | 2 |
| C89×#1288 | 2 |
| #8804 | 89 |