Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#10622524 | C2 | semidirect |
| 2. #13079043 | C2 | semidirect |
| 3. D11×#493 | C2 | semidirect |
| 4. #13070879 | C2 | semidirect |
| 5. #13070872 | C2 | semidirect |
| 6. #13070871 | C2 | semidirect |
| 7. #13070865 | C2 | semidirect |
| 8. C4×#66862 | C2 | semidirect |
| 9. C11×#2246 | C2 | semidirect |
| 16. C2×C11×D16 | C22 | semidirect |
| 18. C11×#493 | C22 | semidirect |
| 20. #10622768 | C22 | semidirect |
| 23. C2×#66891 | C22 | semidirect |
| 24. C2×#66890 | C22 | semidirect |
| 28. C2×#66864 | C22 | semidirect |
| 30. #10622312 | C22 | semidirect |
| 33. C4×C11×C16 | C22 | semidirect |
| 34. #10622140 | C22 | semidirect |
| 35. C4×C11⋊C16 | C22 | semidirect |
| 77. #66862 | D4 | semidirect |
| 121. C11×C16 | C2×D4 | semidirect |
| 122. C11⋊C16 | C2×D4 | semidirect |
| 130. #2246 | D11 | semidirect |
| 175. C2×D16 | C2×D11 | semidirect |
| 185. #493 | C2×D11 | semidirect |
| 190. C4×C16 | C2×D11 | semidirect |
| 201. C4×C11 | #509 | semidirect |
| 298. C16 | D4×D11 | semidirect |
| 299. C11 | #33717 | semidirect |
| 346. C4 | #10622524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622524 | 2 |
| #13079043 | 2 |
| D11×#493 | 2 |
| #13070879 | 2 |
| #13070872 | 2 |
| #13070871 | 2 |
| #13070865 | 2 |
| C4×#66862 | 2 |
| C11×#2246 | 2 |
| #33717 | 11 |