Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
498 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 117 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. #13077468 | C2 | semidirect |
| 2. #13070352 | C2 | semidirect |
| 3. #13070332 | C2 | semidirect |
| 4. #13069515 | C2 | semidirect |
| 5. #13066718 | C2 | semidirect |
| 6. #13066701 | C2 | semidirect |
| 13. C2×C11×SD32 | C4 | semidirect |
| 14. C2×C11×D16 | C4 | semidirect |
| 33. C2×C11×Q16 | C2×C4 | semidirect |
| 39. C2×C11×D8 | C2×C4 | semidirect |
| 54. C2×C11×C16 | C2×C4 | semidirect |
| 162. C2×SD32 | Dic11 | semidirect |
| 163. C2×D16 | Dic11 | semidirect |
| 200. C2×Q16 | C2×Dic11 | semidirect |
| 206. C2×D8 | C2×Dic11 | semidirect |
| 224. C2×C16 | C2×Dic11 | semidirect |
| 288. C11 | #13033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077468 | 2 |
| #13070352 | 2 |
| #13070332 | 2 |
| #13069515 | 2 |
| #13066718 | 2 |
| #13066701 | 2 |
| C2×C11×#509 | 2 |
| #13033 | 11 |