Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
462 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 131 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×D11×Q32 | C2 | semidirect |
| 3. #13070935 | C2 | direct (N × H) |
| 4. C2×#10622160 | C2 | semidirect |
| 5. C2×#10622087 | C2 | semidirect |
| 6. C2×#10622159 | C2 | semidirect |
| 7. C2×#10622085 | C2 | semidirect |
| 8. C2×C11×Q64 | C2 | semidirect |
| 18. D11×Q32 | C22 | semidirect |
| 22. C11×Q64 | C22 | semidirect |
| 24. #10622160 | C22 | semidirect |
| 25. #10622159 | C22 | semidirect |
| 27. #10622087 | C22 | semidirect |
| 28. #10622085 | C22 | semidirect |
| 93. C2×Q64 | D11 | semidirect |
| 135. Q64 | C2×D11 | semidirect |
| 181. C2×C11 | #2264 | semidirect |
| 215. C11 | C2×#2264 | semidirect |
| 253. C2 | #13070935 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622532 | 2 |
| C2×D11×Q32 | 2 |
| #13070935 | 2 |
| C2×#10622160 | 2 |
| C2×#10622087 | 2 |
| C2×#10622159 | 2 |
| C2×#10622085 | 2 |
| C2×C11×Q64 | 2 |
| C2×#2264 | 11 |