Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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. #13070872 | C2 | semidirect |
| 2. #13068234 | C2 | semidirect |
| 4. C8×C11×C16 | C2 | semidirect |
| 33. C11×C16 | D8 | semidirect |
| 37. C8×C16 | D11 | semidirect |
| 45. C8×C11 | SD32 | semidirect |
| 83. C16 | D88 | semidirect |
| 84. C11 | #12517 | semidirect |
| 92. C8 | #66864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070872 | 2 |
| #13068234 | 2 |
| #13068231 | 2 |
| C8×C11×C16 | 2 |
| #12517 | 11 |