Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
182 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26022122 | C2 | semidirect |
| 4. #26018444 | C2 | semidirect |
| 6. #26018387 | C2 | semidirect |
| 7. C89×#1426 | C2 | semidirect |
| 12. Dic1424 | C4 | semidirect |
| 13. #19151437 | C4 | semidirect |
| 87. #1426 | D89 | semidirect |
| 91. C89 | #13657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022572 | 2 |
| #26022137 | 2 |
| #26022122 | 2 |
| #26018444 | 2 |
| #26018438 | 2 |
| #26018387 | 2 |
| C89×#1426 | 2 |
| #13657 | 89 |