Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
618 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 618 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. #13079263 | C2 | semidirect |
| 2. #13079096 | C2 | semidirect |
| 3. #13070880 | C2 | semidirect |
| 4. #13070857 | C2 | semidirect |
| 5. #13070848 | C2 | semidirect |
| 6. #13070669 | C2 | semidirect |
| 7. #13070649 | C2 | semidirect |
| 8. #13070536 | C2 | semidirect |
| 9. #13070526 | C2 | semidirect |
| 10. #13070421 | C2 | semidirect |
| 11. C11×#2246 | C2 | semidirect |
| 18. C2×C11×D16 | C22 | semidirect |
| 20. C11×#493 | C22 | semidirect |
| 27. D8×Dic11 | C22 | semidirect |
| 28. C2×#66891 | 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. #2246 | D11 | semidirect |
| 196. C2×D16 | C2×D11 | semidirect |
| 204. #493 | C2×D11 | semidirect |
| 218. C4×C16 | C2×D11 | semidirect |
| 342. C11 | #33786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079263 | 2 |
| #13079096 | 2 |
| #13070880 | 2 |
| #13070857 | 2 |
| #13070848 | 2 |
| #13070669 | 2 |
| #13070649 | 2 |
| #13070536 | 2 |
| #13070526 | 2 |
| #13070421 | 2 |
| C11×#2246 | 2 |
| #33786 | 11 |