Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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. D16×Dic11 | C2 | semidirect |
| 2. #13066818 | C2 | semidirect |
| 3. #13066794 | C2 | semidirect |
| 4. #13066749 | C2 | semidirect |
| 8. C11×D32 | C4 | semidirect |
| 17. C11×D16 | C2×C4 | semidirect |
| 23. C11×C32 | C2×C4 | semidirect |
| 55. D32 | Dic11 | semidirect |
| 72. D16 | C2×Dic11 | semidirect |
| 79. C32 | C2×Dic11 | semidirect |
| 95. C11 | #13654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D16×Dic11 | 2 |
| #13066818 | 2 |
| #13066794 | 2 |
| #13066749 | 2 |
| C2×C11×D32 | 2 |
| #13654 | 11 |