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. #13079267 | C2 | semidirect |
| 2. #13079098 | C2 | semidirect |
| 3. #13070883 | C2 | semidirect |
| 4. #13070866 | C2 | semidirect |
| 5. #13070859 | C2 | semidirect |
| 6. #13070674 | C2 | semidirect |
| 7. #13070650 | C2 | semidirect |
| 8. #13070542 | C2 | semidirect |
| 9. #13070529 | C2 | semidirect |
| 10. #13070421 | C2 | semidirect |
| 11. C11×#2242 | C2 | semidirect |
| 17. C11×#499 | C22 | semidirect |
| 20. C2×#66892 | C22 | semidirect |
| 27. C2×D176 | C22 | semidirect |
| 29. #10622485 | C22 | semidirect |
| 33. #10622308 | C22 | semidirect |
| 35. C11×#358 | C22 | semidirect |
| 37. C4×C11×C16 | C22 | semidirect |
| 39. Dic11⋊C16 | C22 | semidirect |
| 41. #10622129 | C22 | semidirect |
| 42. #10622099 | C22 | semidirect |
| 145. #2242 | D11 | semidirect |
| 197. #499 | C2×D11 | semidirect |
| 212. #358 | 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 |
|---|---|
| #13079267 | 2 |
| #13079098 | 2 |
| #13070883 | 2 |
| #13070866 | 2 |
| #13070859 | 2 |
| #13070674 | 2 |
| #13070650 | 2 |
| #13070542 | 2 |
| #13070529 | 2 |
| #13070421 | 2 |
| C11×#2242 | 2 |
| #33786 | 11 |