Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2830 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2830 conjugacy classes of subgroups — too many to draw. Only its 747 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×#10622680 | C2 | direct (N × H) |
| 3. C22×#66873 | C2 | semidirect |
| 4. C22×#66867 | C2 | semidirect |
| 5. C22×C11×#125 | C2 | semidirect |
| 9. C2×C11×#125 | C22 | semidirect |
| 16. #10622680 | C22 | direct (N × H) |
| 17. C2×#66873 | C22 | semidirect |
| 18. C2×#66867 | C22 | semidirect |
| 29. C11×#125 | C23 | semidirect |
| 39. #66873 | C23 | semidirect |
| 40. #66867 | C23 | semidirect |
| 67. C22×#125 | D11 | semidirect |
| 96. C2×#125 | C2×D11 | semidirect |
| 103. C22×C11 | #490 | semidirect |
| 128. #125 | C22×D11 | semidirect |
| 136. C2×C11 | C2×#490 | semidirect |
| 164. C11 | C22×#490 | semidirect |
| 187. C22 | #10622680 | direct (N × H) |
| 196. C2 | C2×#10622680 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66927 | 2 |
| C2×#10622680 | 2 |
| C22×#66873 | 2 |
| C22×#66867 | 2 |
| C22×C11×#125 | 2 |
| C22×#490 | 11 |