Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
252 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 63 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×#10622087 | C2 | semidirect |
| 2. C2×#10622158 | C2 | semidirect |
| 3. C2×#10622157 | C2 | semidirect |
| 4. #13070874 | C2 | semidirect |
| 5. #13070864 | C2 | semidirect |
| 6. #13066749 | C2 | semidirect |
| 7. C2×C11×D32 | C2 | semidirect |
| 44. C11×C32 | D4 | semidirect |
| 45. C11⋊C32 | D4 | semidirect |
| 72. C2×D32 | D11 | semidirect |
| 142. C32 | C22⋊D11 | semidirect |
| 170. C11 | #13729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622087 | 2 |
| C2×#10622158 | 2 |
| C2×#10622157 | 2 |
| #13070874 | 2 |
| #13070864 | 2 |
| #13066749 | 2 |
| C2×C11×D32 | 2 |
| #13729 | 11 |