Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
506 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 165 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. #13081622 | C2 | semidirect |
| 3. #13070844 | C2 | semidirect |
| 4. #13070759 | C2 | semidirect |
| 7. Q8×C11×C16 | C2 | semidirect |
| 77. Q8×C16 | D11 | semidirect |
| 80. Q8×C11 | SD32 | semidirect |
| 174. C11 | #33926 | semidirect |
| 179. Q8 | #66864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081622 | 2 |
| Q8×D88 | 2 |
| #13070844 | 2 |
| #13070759 | 2 |
| #13070662 | 2 |
| C4×#66864 | 2 |
| Q8×C11×C16 | 2 |
| #33926 | 11 |