Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3678 conjugacy classes of subgroups; only the 1219 normal subgroups are shown.
This group has 3678 conjugacy classes of subgroups — too many to draw. Only its 1219 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×#10622550 | C2 | semidirect |
| 3. C2×#10622264 | C2 | semidirect |
| 4. D11×#383 | C2 | direct (N × H) |
| 6. C2×C11×#383 | C2 | semidirect |
| 11. C2×C42×D11 | C4 | semidirect |
| 13. C11×#383 | C22 | semidirect |
| 17. #10622550 | C22 | semidirect |
| 19. #10622264 | C22 | semidirect |
| 30. C2×C42×C11 | C2×C4 | semidirect |
| 32. C2×C4×Dic11 | C2×C4 | semidirect |
| 34. C42×D11 | C2×C4 | semidirect |
| 58. C42×C11 | C22×C4 | semidirect |
| 59. C4×Dic11 | C22×C4 | semidirect |
| 64. C2×#383 | D11 | direct (N × H) |
| 93. #383 | C2×D11 | direct (N × H) |
| 102. C2×D11 | #383 | direct (N × H) |
| 122. C2×C42 | C4×D11 | semidirect |
| 127. C2×C11 | C2×#383 | semidirect |
| 130. D11 | C2×#383 | direct (N × H) |
| 151. C42 | C2×C4×D11 | semidirect |
| 152. C11 | C22×#383 | semidirect |
| 184. C2 | D11×#383 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C42×D11 | 2 |
| C2×#10622550 | 2 |
| C2×#10622264 | 2 |
| D11×#383 | 2 |
| C2×D11×#95 | 2 |
| C2×C11×#383 | 2 |
| C22×#383 | 11 |