Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
338 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 69 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. #13081468 | C2 | semidirect |
| 3. #13067973 | C2 | semidirect |
| 4. #13066671 | C2 | semidirect |
| 5. #13066596 | C2 | semidirect |
| 6. #13066578 | C2 | semidirect |
| 7. C11×#2240 | C2 | semidirect |
| 84. D88 | SD16 | semidirect |
| 88. #2240 | D11 | semidirect |
| 117. Dic22 | D16 | semidirect |
| 222. C11 | #12352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081468 | 2 |
| #13070648 | 2 |
| #13067973 | 2 |
| #13066671 | 2 |
| #13066596 | 2 |
| #13066578 | 2 |
| C11×#2240 | 2 |
| #12352 | 11 |