Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
224 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 224 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. #13070524 | C2 | semidirect |
| 4. #13066680 | C2 | semidirect |
| 5. #13066596 | C2 | semidirect |
| 7. C8×C11×C16 | C2 | semidirect |
| 66. C11×C16 | SD16 | semidirect |
| 75. C8×C16 | D11 | semidirect |
| 92. C8×C11 | M32 | semidirect |
| 172. C16 | #4314 | semidirect |
| 173. C11 | #12051 | semidirect |
| 192. C8 | #66862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070524 | 2 |
| #13070449 | 2 |
| C8×#4314 | 2 |
| #13066680 | 2 |
| #13066596 | 2 |
| #13066572 | 2 |
| C8×C11×C16 | 2 |
| #12051 | 11 |