Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26018773 | C2 | semidirect |
| 4. #26018106 | C2 | semidirect |
| 8. #19151528 | C4 | semidirect |
| 10. #19151523 | C4 | semidirect |
| 11. #19151518 | C4 | semidirect |
| 13. #19151510 | C4 | semidirect |
| 190. C89 | #9184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026169 | 2 |
| C4×#15667927 | 2 |
| #26018773 | 2 |
| #26018106 | 2 |
| C89×#2975 | 2 |
| #9184 | 89 |