Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
326 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 107 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×#10622137 | C2 | semidirect |
| 3. #13066805 | C2 | direct (N × H) |
| 4. C2×C11×#368 | C2 | semidirect |
| 15. C11×#368 | C22 | semidirect |
| 17. #10622137 | C22 | semidirect |
| 69. C2×#368 | D11 | semidirect |
| 104. #368 | C2×D11 | semidirect |
| 141. C2×C11 | #1419 | semidirect |
| 169. C11 | C2×#1419 | semidirect |
| 205. C2 | #13066805 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D176 | 2 |
| C2×#10622137 | 2 |
| #13066805 | 2 |
| C2×C11×#368 | 2 |
| C2×#1419 | 11 |