Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
496 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #13070336 | C2 | semidirect |
| 5. #13066713 | C2 | semidirect |
| 6. #13066705 | C2 | semidirect |
| 7. C11×#1979 | C2 | semidirect |
| 17. C2×#66892 | C4 | semidirect |
| 33. C2×C11×Q16 | C2×C4 | semidirect |
| 63. C2×C11⋊C16 | C2×C4 | semidirect |
| 114. #1979 | D11 | semidirect |
| 188. C2×Q16 | C4×D11 | semidirect |
| 269. C11 | #13019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66892 | 2 |
| #13077469 | 2 |
| C2×#10622133 | 2 |
| #13070336 | 2 |
| #13066713 | 2 |
| #13066705 | 2 |
| C11×#1979 | 2 |
| #13019 | 11 |