Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2310 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2310 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 |
|---|---|---|
| 1. C22×#66923 | C2 | semidirect |
| 3. C2×#10622310 | C2 | direct (N × H) |
| 4. C22×#66880 | C2 | semidirect |
| 6. C22×C4×C8×C11 | C2 | semidirect |
| 17. C2×#66923 | C22 | semidirect |
| 18. C2×C4×C8×C11 | C22 | semidirect |
| 20. C2×#66880 | C22 | semidirect |
| 21. #10622310 | C22 | direct (N × H) |
| 44. #66923 | C23 | semidirect |
| 45. C4×C8×C11 | C23 | semidirect |
| 47. #66880 | C23 | semidirect |
| 83. C22×C4×C8 | D11 | semidirect |
| 120. C2×C4×C8 | C2×D11 | semidirect |
| 121. C22×C11 | #488 | semidirect |
| 158. C4×C8 | C22×D11 | semidirect |
| 159. C2×C11 | C2×#488 | semidirect |
| 192. C11 | C22×#488 | semidirect |
| 218. C22 | #10622310 | direct (N × H) |
| 228. C2 | C2×#10622310 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66923 | 2 |
| C22×#66928 | 2 |
| C2×#10622310 | 2 |
| C22×#66880 | 2 |
| C22×#66885 | 2 |
| C22×C4×C8×C11 | 2 |
| C22×#488 | 11 |