Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
224 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 2. #13067514 | C2 | semidirect |
| 4. #13066690 | C2 | semidirect |
| 5. #13066581 | C2 | semidirect |
| 7. C8×C11×C16 | C2 | semidirect |
| 68. C11×C16 | M16 | semidirect |
| 75. C8×C16 | D11 | semidirect |
| 92. C8×C11 | SD32 | semidirect |
| 172. C16 | #4313 | semidirect |
| 173. C11 | #12082 | semidirect |
| 192. C8 | #66864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#66864 | 2 |
| #13067514 | 2 |
| #13067502 | 2 |
| #13066690 | 2 |
| #13066581 | 2 |
| #13066578 | 2 |
| C8×C11×C16 | 2 |
| #12082 | 11 |