Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
242 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 91 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. #13070449 | C2 | semidirect |
| 3. #13066686 | C2 | semidirect |
| 4. #13066572 | C2 | semidirect |
| 5. C8×C11×C16 | C2 | semidirect |
| 48. C11×C16 | D8 | semidirect |
| 54. C8×C16 | D11 | semidirect |
| 67. C8×C11 | M32 | semidirect |
| 127. C16 | D88 | semidirect |
| 128. C11 | #12039 | semidirect |
| 142. C8 | #66862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070449 | 2 |
| C8×D88 | 2 |
| #13066686 | 2 |
| #13066572 | 2 |
| C8×C11×C16 | 2 |
| #12039 | 11 |