Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 1. #13077227 | C2 | semidirect |
| 2. #13070828 | C2 | semidirect |
| 3. #13070388 | C2 | semidirect |
| 4. C2×#10622201 | C2 | semidirect |
| 5. #13070237 | C2 | semidirect |
| 16. #10622738 | C22 | semidirect |
| 21. #10622191 | C22 | semidirect |
| 22. #10622125 | C22 | semidirect |
| 217. C11 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077227 | 2 |
| #13070828 | 2 |
| #13070388 | 2 |
| C2×#10622201 | 2 |
| #13070237 | 2 |
| C11×#3058 | 2 |
| #33657 | 11 |