Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
326 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 81 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. D11×M64 | C2 | semidirect |
| 3. D11×#368 | C2 | semidirect |
| 4. #13066807 | C2 | semidirect |
| 5. #13066806 | C2 | semidirect |
| 6. #13066805 | C2 | semidirect |
| 7. C11×#1419 | C2 | semidirect |
| 18. C11×M64 | C22 | semidirect |
| 19. C11×#368 | C22 | semidirect |
| 20. #10622144 | C22 | semidirect |
| 21. #10622137 | C22 | semidirect |
| 88. #1419 | D11 | direct (N × H) |
| 125. M64 | C2×D11 | semidirect |
| 129. #368 | C2×D11 | semidirect |
| 176. D11 | #1419 | direct (N × H) |
| 206. C11 | C2×#1419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D11×D16 | 2 |
| D11×M64 | 2 |
| D11×#368 | 2 |
| #13066807 | 2 |
| #13066806 | 2 |
| #13066805 | 2 |
| C11×#1419 | 2 |
| C2×#1419 | 11 |