Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
498 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. #13077469 | C2 | semidirect |
| 3. #13070352 | C2 | semidirect |
| 4. #13070331 | C2 | semidirect |
| 5. #13066717 | C2 | semidirect |
| 6. #13066702 | C2 | semidirect |
| 7. C11×#1976 | C2 | semidirect |
| 17. C2×#66892 | C4 | semidirect |
| 18. C2×#66890 | C4 | semidirect |
| 33. C2×C11×Q16 | C2×C4 | semidirect |
| 35. C2×C11×D8 | C2×C4 | semidirect |
| 66. C2×C11⋊C16 | C2×C4 | semidirect |
| 120. #1976 | D11 | semidirect |
| 200. C2×Q16 | C4×D11 | semidirect |
| 208. C2×D8 | C4×D11 | semidirect |
| 288. C11 | #13033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622806 | 2 |
| #13077469 | 2 |
| #13070352 | 2 |
| #13070331 | 2 |
| #13066717 | 2 |
| #13066702 | 2 |
| C11×#1976 | 2 |
| #13033 | 11 |