Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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. #13070768 | C2 | semidirect |
| 4. #13066680 | C2 | semidirect |
| 5. #13066675 | C2 | semidirect |
| 7. C8×C11×Q16 | C2 | semidirect |
| 52. C11×Q16 | SD16 | semidirect |
| 74. C8×Q16 | D11 | semidirect |
| 159. Q16 | #4314 | semidirect |
| 178. C11 | #12419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070768 | 2 |
| #13070656 | 2 |
| #13068208 | 2 |
| #13066680 | 2 |
| #13066675 | 2 |
| #13066661 | 2 |
| C8×C11×Q16 | 2 |
| #12419 | 11 |