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 |
|---|---|---|
| 2. C2×#10622681 | C2 | direct (N × H) |
| 3. C22×#66874 | C2 | semidirect |
| 5. C22×C4×C11⋊C8 | C2 | semidirect |
| 6. C22×C11×#125 | C2 | semidirect |
| 10. C2×C11×#125 | C22 | semidirect |
| 18. #10622681 | C22 | direct (N × H) |
| 19. C2×#66874 | C22 | semidirect |
| 21. C2×C4×C11⋊C8 | C22 | semidirect |
| 34. C11×#125 | C23 | semidirect |
| 45. #66874 | C23 | semidirect |
| 47. C4×C11⋊C8 | C23 | semidirect |
| 78. C22×#125 | D11 | semidirect |
| 110. C2×#125 | C2×D11 | semidirect |
| 121. C22×C11 | #488 | semidirect |
| 147. #125 | C22×D11 | semidirect |
| 159. C2×C11 | C2×#488 | semidirect |
| 192. C11 | C22×#488 | semidirect |
| 218. C22 | #10622681 | direct (N × H) |
| 228. C2 | C2×#10622681 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66928 | 2 |
| C2×#10622681 | 2 |
| C22×#66874 | 2 |
| C22×#66873 | 2 |
| C22×C4×C11⋊C8 | 2 |
| C22×C11×#125 | 2 |
| C22×#488 | 11 |