Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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. #13081718 | C2 | semidirect |
| 3. #13070344 | C2 | semidirect |
| 4. #13068663 | C2 | semidirect |
| 5. #13066716 | C2 | semidirect |
| 6. #13066715 | C2 | semidirect |
| 7. C11×#2143 | C2 | semidirect |
| 54. C2×C11×C16 | D4 | semidirect |
| 67. C2×C11⋊C16 | D4 | semidirect |
| 125. #2143 | D11 | semidirect |
| 233. C2×C16 | C22⋊D11 | semidirect |
| 301. C11 | #13076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081718 | 2 |
| #13078274 | 2 |
| #13070344 | 2 |
| #13068663 | 2 |
| #13066716 | 2 |
| #13066715 | 2 |
| C11×#2143 | 2 |
| #13076 | 11 |