Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
826 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 219 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. C22×#66893 | C2 | semidirect |
| 4. #13070885 | C2 | direct (N × H) |
| 5. C2×#10622099 | C2 | semidirect |
| 6. C2×C11×#494 | C2 | semidirect |
| 15. C11×#494 | C22 | semidirect |
| 18. C2×#66893 | C22 | semidirect |
| 24. #10622099 | C22 | semidirect |
| 97. C2×#494 | D11 | semidirect |
| 141. #494 | C2×D11 | semidirect |
| 188. C2×C11 | #2251 | semidirect |
| 228. C11 | C2×#2251 | semidirect |
| 268. C2 | #13070885 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66893 | 2 |
| C22×#66892 | 2 |
| C2×#10622309 | 2 |
| #13070885 | 2 |
| C2×#10622099 | 2 |
| C2×C11×#494 | 2 |
| C2×#2251 | 11 |