Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
334 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 67 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×D176 | C2 | semidirect |
| 2. C2×D352 | C2 | semidirect |
| 3. #13070702 | C2 | semidirect |
| 4. #13066795 | C2 | semidirect |
| 5. C11×C22⋊C32 | C2 | semidirect |
| 12. C2×D176 | C22 | semidirect |
| 13. C2×C11×C32 | C22 | semidirect |
| 15. #10622142 | C22 | semidirect |
| 33. D176 | D4 | semidirect |
| 61. C22⋊C32 | D11 | semidirect |
| 90. C2×C32 | C2×D11 | semidirect |
| 95. C22×C11 | D32 | semidirect |
| 153. C11 | #13661 | semidirect |
| 183. C22 | D352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D176 | 2 |
| C2×D352 | 2 |
| #13070702 | 2 |
| #13066795 | 2 |
| C11×C22⋊C32 | 2 |
| #13661 | 11 |