Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
494 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 107 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. #13077490 | C2 | semidirect |
| 3. C2×#10622135 | C2 | semidirect |
| 4. C2×#10622129 | C2 | semidirect |
| 5. #13069524 | C2 | semidirect |
| 6. #13066706 | C2 | semidirect |
| 7. C11×#1387 | C2 | semidirect |
| 20. #10622521 | C4 | semidirect |
| 46. C2×D88 | C2×C4 | semidirect |
| 54. C11×M32 | C2×C4 | semidirect |
| 129. #1387 | D11 | semidirect |
| 237. M32 | C4×D11 | semidirect |
| 311. C11 | #13022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622521 | 2 |
| #13077490 | 2 |
| C2×#10622135 | 2 |
| C2×#10622129 | 2 |
| #13069524 | 2 |
| #13066706 | 2 |
| C11×#1387 | 2 |
| #13022 | 11 |