Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
294 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 81 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. C2×D11×C32 | C2 | semidirect |
| 3. D11×#368 | C2 | semidirect |
| 4. #13066801 | C2 | semidirect |
| 5. #13066800 | C2 | semidirect |
| 6. #13066799 | C2 | semidirect |
| 7. C11×#1417 | C2 | semidirect |
| 20. C2×C11×C32 | C22 | semidirect |
| 21. C11×#368 | C22 | semidirect |
| 22. #10622144 | C22 | semidirect |
| 23. C2×C11⋊C32 | C22 | semidirect |
| 102. #1417 | D11 | direct (N × H) |
| 147. C2×C32 | C2×D11 | semidirect |
| 150. #368 | C2×D11 | semidirect |
| 202. D11 | #1417 | direct (N × H) |
| 238. C11 | C2×#1417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D11×#508 | 2 |
| C2×D11×C32 | 2 |
| D11×#368 | 2 |
| #13066801 | 2 |
| #13066800 | 2 |
| #13066799 | 2 |
| C11×#1417 | 2 |
| C2×#1417 | 11 |