Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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. #13077501 | C2 | semidirect |
| 3. #13070353 | C2 | semidirect |
| 4. C2×#10622156 | C2 | semidirect |
| 5. #13069514 | C2 | semidirect |
| 6. #13066722 | C2 | semidirect |
| 7. C11×#1378 | C2 | semidirect |
| 20. #10622522 | C4 | semidirect |
| 22. #10622521 | C4 | semidirect |
| 36. C2×Dic44 | C2×C4 | semidirect |
| 46. C2×D88 | C2×C4 | semidirect |
| 58. C11×M32 | C2×C4 | semidirect |
| 135. #1378 | D11 | semidirect |
| 245. M32 | C4×D11 | semidirect |
| 317. C11 | #13030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081752 | 2 |
| #13077501 | 2 |
| #13070353 | 2 |
| C2×#10622156 | 2 |
| #13069514 | 2 |
| #13066722 | 2 |
| C11×#1378 | 2 |
| #13030 | 11 |