Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
200 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 200 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. Q32×Dic11 | C2 | semidirect |
| 3. #13066816 | C2 | semidirect |
| 4. #13066797 | C2 | semidirect |
| 6. #13066749 | C2 | semidirect |
| 12. C11×SD64 | C4 | semidirect |
| 25. C11×Q32 | C2×C4 | semidirect |
| 35. C11×C32 | C2×C4 | semidirect |
| 82. SD64 | Dic11 | semidirect |
| 106. Q32 | C2×Dic11 | semidirect |
| 117. C32 | C2×Dic11 | semidirect |
| 140. C11 | #13652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×Dic11 | 2 |
| D16×Dic11 | 2 |
| #13066816 | 2 |
| #13066797 | 2 |
| #13066794 | 2 |
| #13066749 | 2 |
| C2×C11×SD64 | 2 |
| #13652 | 11 |