Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 99 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. #13068367 | C2 | semidirect |
| 3. #13067232 | C2 | semidirect |
| 5. #13067129 | C2 | semidirect |
| 7. C11×#1568 | C2 | semidirect |
| 17. #10622307 | C4 | semidirect |
| 18. #10622306 | C4 | semidirect |
| 21. #10622294 | C4 | semidirect |
| 22. #10622293 | C4 | semidirect |
| 121. #1568 | D11 | semidirect |
| 294. C11 | #9766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079175 | 2 |
| #13068367 | 2 |
| #13067232 | 2 |
| #13067228 | 2 |
| #13067129 | 2 |
| #13067125 | 2 |
| C11×#1568 | 2 |
| #9766 | 11 |