Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
756 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26021926 | C2 | semidirect |
| 3. #26021923 | C2 | semidirect |
| 4. #26020777 | C2 | semidirect |
| 5. #26020772 | C2 | semidirect |
| 6. #26020636 | C2 | semidirect |
| 7. C89×#2126 | C2 | semidirect |
| 9. #19152347 | C4 | semidirect |
| 11. #19152310 | C4 | semidirect |
| 289. #2126 | D89 | semidirect |
| 293. C89 | #12780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034679 | 2 |
| #26021926 | 2 |
| #26021923 | 2 |
| #26020777 | 2 |
| #26020772 | 2 |
| #26020636 | 2 |
| C89×#2126 | 2 |
| #12780 | 89 |