Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
134 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 51 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. #13066830 | C2 | direct (N × H) |
| 3. C2×C11⋊C64 | C2 | semidirect |
| 4. C2×C11×Q64 | C2 | semidirect |
| 8. C11×Q64 | C22 | semidirect |
| 12. C11⋊C64 | C22 | semidirect |
| 32. C2×Q64 | D11 | semidirect |
| 48. Q64 | C2×D11 | semidirect |
| 68. C2×C11 | SD128 | semidirect |
| 80. C11 | C2×SD128 | semidirect |
| 97. C2 | #13066830 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D352 | 2 |
| #13066830 | 2 |
| C2×C11⋊C64 | 2 |
| C2×C11×Q64 | 2 |
| C2×SD128 | 11 |