Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
598 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 105 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. #13079734 | C2 | semidirect |
| 2. #13079076 | C2 | semidirect |
| 3. #13069567 | C2 | semidirect |
| 4. #13069536 | C2 | semidirect |
| 5. #13067111 | C2 | semidirect |
| 6. #13066466 | C2 | semidirect |
| 129. #4318 | D8 | semidirect |
| 334. C11 | #10204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079734 | 2 |
| #13079076 | 2 |
| #13069567 | 2 |
| #13069536 | 2 |
| #13067111 | 2 |
| #13066466 | 2 |
| C11×#3245 | 2 |
| #10204 | 11 |