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 |
|---|---|---|
| 2. #13070830 | C2 | semidirect |
| 3. #13070390 | C2 | semidirect |
| 4. C2×#10622133 | C2 | semidirect |
| 5. #13070237 | C2 | semidirect |
| 6. C11×#2916 | C2 | semidirect |
| 12. C11×#430 | C22 | semidirect |
| 20. #10622191 | C22 | semidirect |
| 22. #10622132 | C22 | semidirect |
| 89. #2916 | D11 | semidirect |
| 127. #430 | C2×D11 | semidirect |
| 217. C11 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13078264 | 2 |
| #13070830 | 2 |
| #13070390 | 2 |
| C2×#10622133 | 2 |
| #13070237 | 2 |
| C11×#2916 | 2 |
| #33657 | 11 |