Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
954 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 159 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. #26018138 | C2 | semidirect |
| 4. #26018137 | C2 | semidirect |
| 5. C89×#1297 | C2 | semidirect |
| 7. C2×M16×D89 | C4 | semidirect |
| 10. #19151561 | C4 | semidirect |
| 13. #19151460 | C4 | semidirect |
| 14. #19151457 | C4 | semidirect |
| 190. #1297 | D89 | semidirect |
| 191. C89 | #8049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #407×D89 | 2 |
| #26022633 | 2 |
| #26018138 | 2 |
| #26018137 | 2 |
| C89×#1297 | 2 |
| #8049 | 89 |