Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 2. C2×Dic176 | C2 | semidirect |
| 3. Dic352 | C2 | semidirect |
| 4. #13066832 | C2 | semidirect |
| 5. C11×M128 | C2 | semidirect |
| 40. M128 | D11 | semidirect |
| 89. C11 | #13743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070925 | 2 |
| C2×Dic176 | 2 |
| Dic352 | 2 |
| #13066832 | 2 |
| C11×M128 | 2 |
| #13743 | 11 |