Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
472 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 81. Q8×C11 | Q32 | semidirect |
| 168. C11 | #33930 | semidirect |
| 174. Q8 | #66893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081622 | 2 |
| #13070845 | 2 |
| #13070765 | 2 |
| #13070666 | 2 |
| Q8×C11⋊C16 | 2 |
| C4×#66893 | 2 |
| Q8×C11×Q16 | 2 |
| #33930 | 11 |