Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
748 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26021083 | C2 | semidirect |
| 3. #26018972 | C2 | semidirect |
| 4. #26018886 | C2 | semidirect |
| 5. #26018764 | C2 | semidirect |
| 6. #26018761 | C2 | semidirect |
| 7. C89×#1559 | C2 | semidirect |
| 10. #19152308 | C4 | semidirect |
| 12. #19152270 | C4 | semidirect |
| 224. #1559 | D89 | semidirect |
| 229. C89 | #8493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034652 | 2 |
| #26021083 | 2 |
| #26018972 | 2 |
| #26018886 | 2 |
| #26018764 | 2 |
| #26018761 | 2 |
| C89×#1559 | 2 |
| #8493 | 89 |