Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
492 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 135 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. #13081038 | C2 | semidirect |
| 2. #13070810 | C2 | semidirect |
| 3. #13070760 | C2 | semidirect |
| 4. #13070703 | C2 | semidirect |
| 5. C4×D176 | C2 | semidirect |
| 6. C16×D44 | C2 | semidirect |
| 7. #13070397 | C2 | semidirect |
| 8. C11×#2252 | C2 | semidirect |
| 80. #2252 | D11 | semidirect |
| 195. C11 | #33908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081038 | 2 |
| #13070810 | 2 |
| #13070760 | 2 |
| #13070703 | 2 |
| C4×D176 | 2 |
| C16×D44 | 2 |
| #13070397 | 2 |
| C11×#2252 | 2 |
| #33908 | 11 |