Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
528 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 167 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. #13070841 | C2 | semidirect |
| 3. #13070760 | C2 | semidirect |
| 4. #13070656 | C2 | semidirect |
| 5. Q8×C11⋊C16 | C2 | semidirect |
| 6. C4×#66892 | C2 | semidirect |
| 7. Q8×C11×Q16 | C2 | semidirect |
| 56. C11×Q16 | #41 | semidirect |
| 73. Q8×Q16 | D11 | semidirect |
| 83. Q8×C11 | SD32 | semidirect |
| 160. Q16 | #4343 | semidirect |
| 176. C11 | #33929 | semidirect |
| 181. Q8 | #66892 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081591 | 2 |
| #13070841 | 2 |
| #13070760 | 2 |
| #13070656 | 2 |
| Q8×C11⋊C16 | 2 |
| C4×#66892 | 2 |
| Q8×C11×Q16 | 2 |
| #33929 | 11 |