Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
214 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 75 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. C4×D176 | C2 | semidirect |
| 3. #13066816 | C2 | semidirect |
| 4. #13066795 | C2 | semidirect |
| 5. C4×C11×C32 | C2 | semidirect |
| 13. D352 | C4 | direct (N × H) |
| 22. D176 | C2×C4 | semidirect |
| 24. C11×C32 | C2×C4 | semidirect |
| 42. C4×C32 | D11 | semidirect |
| 67. C4×C11 | D32 | semidirect |
| 81. C32 | C4×D11 | semidirect |
| 98. C11 | C4×D32 | semidirect |
| 116. C4 | D352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D352 | 2 |
| C4×D176 | 2 |
| #13066816 | 2 |
| #13066795 | 2 |
| C4×C11×C32 | 2 |
| C4×D32 | 11 |