Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
462 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 155 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. C22×Dic88 | C2 | semidirect |
| 3. #13070936 | C2 | direct (N × H) |
| 4. C2×Dic176 | C2 | semidirect |
| 5. C2×#10622087 | C2 | semidirect |
| 6. C2×C11×M64 | C2 | semidirect |
| 14. C2×Dic88 | C22 | semidirect |
| 19. C11×M64 | C22 | semidirect |
| 21. Dic176 | C22 | semidirect |
| 22. #10622087 | C22 | semidirect |
| 81. C2×M64 | D11 | semidirect |
| 117. M64 | C2×D11 | semidirect |
| 155. C2×C11 | #2264 | semidirect |
| 185. C11 | C2×#2264 | semidirect |
| 219. C2 | #13070936 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622517 | 2 |
| C22×Dic88 | 2 |
| #13070936 | 2 |
| C2×Dic176 | 2 |
| C2×#10622087 | 2 |
| C2×C11×M64 | 2 |
| C2×#2264 | 11 |