Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 2. C2×#10622151 | C2 | semidirect |
| 5. #13069369 | C2 | semidirect |
| 6. #13066722 | C2 | semidirect |
| 7. C11×#1375 | C2 | semidirect |
| 23. #10622147 | C4 | semidirect |
| 46. C2×C11×C16 | C2×C4 | semidirect |
| 52. #66882 | C2×C4 | semidirect |
| 102. #1375 | D11 | semidirect |
| 185. C2×C16 | C4×D11 | semidirect |
| 239. C11 | #12956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622324 | 2 |
| C2×#10622151 | 2 |
| C2×#10622154 | 2 |
| #13070333 | 2 |
| #13069369 | 2 |
| #13066722 | 2 |
| C11×#1375 | 2 |
| #12956 | 11 |