Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
854 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 203 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×Dic88 | C2 | semidirect |
| 2. C22×#66891 | C2 | semidirect |
| 3. C2×#10622768 | C2 | semidirect |
| 4. #13070874 | C2 | direct (N × H) |
| 5. C2×C16×Dic11 | C2 | semidirect |
| 15. #10622768 | C22 | semidirect |
| 17. C2×#66891 | C22 | semidirect |
| 21. C2×Dic88 | C22 | semidirect |
| 22. C16×Dic11 | C22 | semidirect |
| 164. C2×C11 | #2249 | semidirect |
| 197. C11 | C2×#2249 | semidirect |
| 232. C2 | #13070874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic88 | 2 |
| C22×#66891 | 2 |
| C2×#10622768 | 2 |
| #13070874 | 2 |
| C2×C16×Dic11 | 2 |
| C22×C11×D16 | 2 |
| C2×#2249 | 11 |