Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26018890 | C2 | semidirect |
| 5. #26018125 | C2 | semidirect |
| 6. #26018116 | C2 | semidirect |
| 7. C89×#1515 | C2 | semidirect |
| 9. #19152001 | C4 | semidirect |
| 10. #19151972 | C4 | semidirect |
| 11. #19151948 | C4 | semidirect |
| 12. #19151946 | C4 | semidirect |
| 163. #1515 | D89 | semidirect |
| 167. C89 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030971 | 2 |
| #26029322 | 2 |
| #26018890 | 2 |
| #26018798 | 2 |
| #26018125 | 2 |
| #26018116 | 2 |
| C89×#1515 | 2 |
| #9415 | 89 |