Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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. #13067513 | C2 | semidirect |
| 3. #13066690 | C2 | semidirect |
| 4. #13066580 | C2 | semidirect |
| 6. C16×C11⋊C8 | C2 | semidirect |
| 67. C11×C16 | M16 | semidirect |
| 96. C11⋊C8 | SD32 | semidirect |
| 172. C16 | #4318 | semidirect |
| 173. C11 | #12082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13067513 | 2 |
| #13067501 | 2 |
| #13066690 | 2 |
| #13066580 | 2 |
| #13066577 | 2 |
| C16×C11⋊C8 | 2 |
| C4×C11×SD32 | 2 |
| #12082 | 11 |