Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
456 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. C2×#10622316 | C2 | semidirect |
| 4. #13067334 | C2 | semidirect |
| 6. #13066971 | C2 | semidirect |
| 7. C11×#1302 | C2 | semidirect |
| 123. #1302 | D11 | semidirect |
| 284. C11 | #10134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079808 | 2 |
| #13079746 | 2 |
| C2×#10622316 | 2 |
| #13067334 | 2 |
| #13067226 | 2 |
| #13066971 | 2 |
| C11×#1302 | 2 |
| #10134 | 11 |