Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
480 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 123 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. #13070198 | C2 | semidirect |
| 2. #13070191 | C2 | semidirect |
| 3. #13070072 | C2 | semidirect |
| 5. #13069320 | C2 | semidirect |
| 7. #13068855 | C2 | semidirect |
| 8. #13068837 | C2 | semidirect |
| 9. C11×#1837 | C2 | semidirect |
| 107. #1837 | D11 | semidirect |
| 237. C11 | #32702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070198 | 2 |
| #13070191 | 2 |
| #13070072 | 2 |
| #13069903 | 2 |
| #13069320 | 2 |
| #13068979 | 2 |
| #13068855 | 2 |
| #13068837 | 2 |
| C11×#1837 | 2 |
| #32702 | 11 |