Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 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×#10622808 | C2 | semidirect |
| 2. C22×#66864 | C2 | semidirect |
| 4. #13077483 | C2 | semidirect |
| 5. #13070681 | C2 | semidirect |
| 6. #13070655 | C2 | semidirect |
| 7. #13070374 | C2 | semidirect |
| 8. #13070331 | C2 | semidirect |
| 9. C11×#2138 | C2 | semidirect |
| 20. C2×#66893 | C22 | semidirect |
| 23. C2×#66891 | C22 | semidirect |
| 29. #10622486 | C22 | semidirect |
| 31. C11×#358 | C22 | semidirect |
| 32. C11×#357 | C22 | semidirect |
| 33. Dic11⋊C16 | C22 | semidirect |
| 56. C2×Dic44 | D4 | semidirect |
| 134. #2138 | D11 | semidirect |
| 188. #358 | C2×D11 | semidirect |
| 190. #357 | C2×D11 | semidirect |
| 301. C11 | #33587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622808 | 2 |
| C22×#66864 | 2 |
| #13079103 | 2 |
| #13077483 | 2 |
| #13070681 | 2 |
| #13070655 | 2 |
| #13070374 | 2 |
| #13070331 | 2 |
| C11×#2138 | 2 |
| #33587 | 11 |