Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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. #13077469 | C2 | semidirect |
| 3. C2×#10622154 | C2 | semidirect |
| 4. #13070333 | C2 | semidirect |
| 5. #13069526 | C2 | semidirect |
| 6. #13066712 | C2 | semidirect |
| 7. C11×#1379 | C2 | semidirect |
| 21. C2×D176 | C4 | semidirect |
| 42. C2×D88 | C2×C4 | semidirect |
| 53. C2×C11×C16 | C2×C4 | semidirect |
| 116. #1379 | D11 | semidirect |
| 213. C2×C16 | C4×D11 | semidirect |
| 274. C11 | #13017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D176 | 2 |
| #13077469 | 2 |
| C2×#10622154 | 2 |
| #13070333 | 2 |
| #13069526 | 2 |
| #13066712 | 2 |
| C11×#1379 | 2 |
| #13017 | 11 |