Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
622 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26022869 | C2 | semidirect |
| 4. C2×#19151323 | C2 | semidirect |
| 5. #26018120 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 12. #19151529 | C4 | semidirect |
| 14. #19151512 | C4 | semidirect |
| 236. C89 | #9204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025996 | 2 |
| #26022869 | 2 |
| #26018820 | 2 |
| C2×#19151323 | 2 |
| #26018120 | 2 |
| #26018119 | 2 |
| C89×#1519 | 2 |
| #9204 | 89 |