Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2830 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2830 conjugacy classes of subgroups — too many to draw. Only its 747 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×#66923 | C2 | semidirect |
| 2. C2×#10622684 | C2 | direct (N × H) |
| 3. C22×#66896 | C2 | semidirect |
| 4. C22×#66867 | C2 | semidirect |
| 15. C2×#66923 | C22 | semidirect |
| 16. C2×#66896 | C22 | semidirect |
| 17. #10622684 | C22 | direct (N × H) |
| 18. C2×#66867 | C22 | semidirect |
| 38. #66923 | C23 | semidirect |
| 39. #66896 | C23 | semidirect |
| 40. #66867 | C23 | semidirect |
| 106. C22×C11 | #490 | semidirect |
| 137. C2×C11 | C2×#490 | semidirect |
| 164. C11 | C22×#490 | semidirect |
| 187. C22 | #10622684 | direct (N × H) |
| 196. C2 | C2×#10622684 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66923 | 2 |
| C2×#10622684 | 2 |
| C22×#66896 | 2 |
| C22×#66867 | 2 |
| C22×C11×#127 | 2 |
| C22×#490 | 11 |