Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #26021203 | C2 | semidirect |
| 3. #26018977 | C2 | semidirect |
| 5. #26018122 | C2 | semidirect |
| 6. #26018109 | C2 | semidirect |
| 9. #19152008 | C4 | semidirect |
| 10. #19151957 | C4 | semidirect |
| 196. C89 | #9375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031470 | 2 |
| #26021203 | 2 |
| #26018977 | 2 |
| #26018777 | 2 |
| #26018122 | 2 |
| #26018109 | 2 |
| C89×#2992 | 2 |
| #9375 | 89 |