Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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×#10622719 | C2 | semidirect |
| 2. #13070821 | C2 | semidirect |
| 3. #13070804 | C2 | semidirect |
| 4. #13070405 | C2 | semidirect |
| 5. #13070328 | C2 | semidirect |
| 6. #13070227 | C2 | semidirect |
| 22. #10622202 | C22 | semidirect |
| 23. #10622200 | C22 | semidirect |
| 25. #10622128 | C22 | semidirect |
| 26. #10622127 | C22 | semidirect |
| 237. C11 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622719 | 2 |
| #13070821 | 2 |
| #13070804 | 2 |
| #13070405 | 2 |
| #13070328 | 2 |
| #13070227 | 2 |
| C11×#3050 | 2 |
| #33647 | 11 |