Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 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. #13077533 | C2 | semidirect |
| 2. C2×#10622201 | C2 | semidirect |
| 3. #13070344 | C2 | semidirect |
| 4. #13069527 | C2 | semidirect |
| 5. #13066720 | C2 | semidirect |
| 6. #13066701 | C2 | semidirect |
| 13. C2×C11×SD32 | C4 | semidirect |
| 14. C2×C11×D16 | C4 | semidirect |
| 161. C2×SD32 | Dic11 | semidirect |
| 162. C2×D16 | Dic11 | semidirect |
| 285. C11 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077533 | 2 |
| C2×#10622201 | 2 |
| #13070344 | 2 |
| #13069527 | 2 |
| #13066720 | 2 |
| #13066701 | 2 |
| C2×C11×#509 | 2 |
| #13036 | 11 |