Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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. D11×Q64 | C2 | semidirect |
| 3. #13066832 | C2 | semidirect |
| 4. #13066831 | C2 | semidirect |
| 5. #13066830 | C2 | semidirect |
| 6. D11×C64 | C2 | semidirect |
| 7. C11×SD128 | C2 | semidirect |
| 10. C11×Q64 | C22 | semidirect |
| 14. Dic176 | C22 | semidirect |
| 17. C11×C64 | C22 | semidirect |
| 18. C11⋊C64 | C22 | semidirect |
| 47. SD128 | D11 | direct (N × H) |
| 64. Q64 | C2×D11 | semidirect |
| 70. C64 | C2×D11 | semidirect |
| 93. D11 | SD128 | direct (N × H) |
| 105. C11 | C2×SD128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D11×Q64 | 2 |
| D11×D32 | 2 |
| #13066832 | 2 |
| #13066831 | 2 |
| #13066830 | 2 |
| D11×C64 | 2 |
| C11×SD128 | 2 |
| C2×SD128 | 11 |