Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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. #13081754 | C2 | semidirect |
| 2. #13080416 | C2 | semidirect |
| 3. #13070866 | C2 | semidirect |
| 4. #13070737 | C2 | semidirect |
| 5. #13070692 | C2 | semidirect |
| 6. #13070574 | C2 | semidirect |
| 7. #13070454 | C2 | semidirect |
| 8. C11×#2178 | C2 | semidirect |
| 9. #10623300 | C22 | semidirect |
| 12. C11×#443 | C22 | semidirect |
| 13. #10622806 | C22 | semidirect |
| 18. C2×D176 | C22 | semidirect |
| 19. C2×D176 | C22 | semidirect |
| 20. #10622514 | C22 | semidirect |
| 21. #10622510 | C22 | semidirect |
| 24. #10622308 | C22 | semidirect |
| 25. C11×#368 | C22 | semidirect |
| 26. C11×#359 | C22 | semidirect |
| 27. C4×C11×C16 | C22 | semidirect |
| 28. #10622146 | C22 | semidirect |
| 29. #10622133 | C22 | semidirect |
| 30. #10622101 | C22 | semidirect |
| 47. C11×Q32 | D4 | semidirect |
| 48. C11×SD32 | D4 | semidirect |
| 49. C11×D16 | D4 | semidirect |
| 109. #2178 | D11 | semidirect |
| 150. #443 | C2×D11 | semidirect |
| 151. #368 | C2×D11 | semidirect |
| 154. #359 | C2×D11 | semidirect |
| 156. C4×C16 | C2×D11 | semidirect |
| 184. Q32 | D44 | semidirect |
| 186. SD32 | D44 | semidirect |
| 191. D16 | D44 | semidirect |
| 244. C11 | #33858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081754 | 2 |
| #13080416 | 2 |
| #13070866 | 2 |
| #13070737 | 2 |
| #13070692 | 2 |
| #13070574 | 2 |
| #13070454 | 2 |
| C11×#2178 | 2 |
| #33858 | 11 |