Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
668 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 1. #13081757 | C2 | semidirect |
| 2. #13080416 | C2 | semidirect |
| 3. #13070866 | C2 | semidirect |
| 4. #13070736 | C2 | semidirect |
| 5. #13070693 | C2 | semidirect |
| 6. #13070575 | C2 | semidirect |
| 7. #13070498 | C2 | semidirect |
| 8. C11×#2170 | C2 | semidirect |
| 10. #10623283 | C22 | semidirect |
| 11. C11×#504 | C22 | semidirect |
| 13. #10622755 | C22 | semidirect |
| 15. #10622521 | C22 | semidirect |
| 19. C2×D176 | C22 | semidirect |
| 20. C2×D176 | C22 | semidirect |
| 23. #10622313 | C22 | semidirect |
| 24. #10622308 | C22 | semidirect |
| 25. C11×#364 | C22 | semidirect |
| 26. C11×#350 | C22 | semidirect |
| 27. C4×C11×C16 | C22 | semidirect |
| 28. #10622154 | C22 | semidirect |
| 29. #10622148 | C22 | semidirect |
| 30. #10622144 | C22 | semidirect |
| 58. Dic88 | D4 | semidirect |
| 60. #66864 | D4 | semidirect |
| 65. D176 | D4 | semidirect |
| 110. #2170 | D11 | semidirect |
| 144. #504 | C2×D11 | semidirect |
| 152. #364 | C2×D11 | semidirect |
| 155. #350 | C2×D11 | semidirect |
| 156. C4×C16 | C2×D11 | semidirect |
| 244. C11 | #33858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081757 | 2 |
| #13080416 | 2 |
| #13070866 | 2 |
| #13070736 | 2 |
| #13070693 | 2 |
| #13070575 | 2 |
| #13070498 | 2 |
| C11×#2170 | 2 |
| #33858 | 11 |