Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
212 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 71 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. C4×D176 | C2 | semidirect |
| 3. #13066817 | C2 | semidirect |
| 4. #13066794 | C2 | semidirect |
| 5. #13066793 | C2 | semidirect |
| 6. #13066750 | C2 | semidirect |
| 7. C4×C11×D16 | C2 | semidirect |
| 15. #10622157 | C4 | semidirect |
| 25. C11×D16 | C2×C4 | semidirect |
| 34. D176 | C2×C4 | semidirect |
| 36. C11⋊C32 | C2×C4 | semidirect |
| 58. C4×D16 | D11 | semidirect |
| 111. D16 | C4×D11 | semidirect |
| 144. C11 | #13654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622157 | 2 |
| C4×D176 | 2 |
| #13066817 | 2 |
| #13066794 | 2 |
| #13066793 | 2 |
| #13066750 | 2 |
| C4×C11×D16 | 2 |
| #13654 | 11 |