Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
194 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 83 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. #13066817 | C2 | semidirect |
| 5. #13066816 | C2 | semidirect |
| 6. #13066815 | C2 | semidirect |
| 7. C11×#1424 | C2 | semidirect |
| 19. #10622085 | C4 | semidirect |
| 33. C11×C32 | C2×C4 | semidirect |
| 34. C11⋊C32 | C2×C4 | semidirect |
| 56. #1424 | D11 | semidirect |
| 109. C32 | C4×D11 | semidirect |
| 130. C11 | #13634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622085 | 2 |
| #13070397 | 2 |
| D11×#366 | 2 |
| #13066817 | 2 |
| #13066816 | 2 |
| #13066815 | 2 |
| C11×#1424 | 2 |
| #13634 | 11 |