Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
594 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 131 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. #13079272 | C2 | semidirect |
| 3. #13070885 | C2 | semidirect |
| 4. #13070857 | C2 | semidirect |
| 5. #13070848 | C2 | semidirect |
| 6. #13070676 | C2 | semidirect |
| 7. #13070654 | C2 | semidirect |
| 8. #13070553 | C2 | semidirect |
| 9. #13070543 | C2 | semidirect |
| 10. #13070421 | C2 | semidirect |
| 11. C11×#2248 | C2 | semidirect |
| 18. C2×C11×SD32 | C22 | semidirect |
| 19. C11×#494 | C22 | semidirect |
| 24. Q16×Dic11 | C22 | semidirect |
| 25. C2×#66893 | C22 | semidirect |
| 34. #10622296 | C22 | semidirect |
| 35. C4×C11×C16 | C22 | semidirect |
| 37. #10622200 | C22 | semidirect |
| 40. #10622141 | C22 | semidirect |
| 41. Dic11⋊C16 | C22 | semidirect |
| 42. #10622099 | C22 | semidirect |
| 143. #2248 | D11 | semidirect |
| 193. C2×SD32 | C2×D11 | semidirect |
| 199. #494 | C2×D11 | semidirect |
| 215. C4×C16 | C2×D11 | semidirect |
| 336. C11 | #33788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079272 | 2 |
| #13079096 | 2 |
| #13070885 | 2 |
| #13070857 | 2 |
| #13070848 | 2 |
| #13070676 | 2 |
| #13070654 | 2 |
| #13070553 | 2 |
| #13070543 | 2 |
| #13070421 | 2 |
| C11×#2248 | 2 |
| #33788 | 11 |