Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
284 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 99 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. #13070898 | C2 | semidirect |
| 3. #13070844 | C2 | semidirect |
| 5. #13068213 | C2 | semidirect |
| 7. C8×C11×C16 | C2 | semidirect |
| 69. C11×C16 | SD16 | semidirect |
| 76. C8×C16 | D11 | semidirect |
| 93. C8×C11 | SD32 | semidirect |
| 171. C16 | #4314 | semidirect |
| 172. C11 | #12505 | semidirect |
| 189. C8 | #66864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070898 | 2 |
| #13070872 | 2 |
| #13070844 | 2 |
| #13070840 | 2 |
| #13068213 | 2 |
| #13068208 | 2 |
| C8×C11×C16 | 2 |
| #12505 | 11 |