Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3798 conjugacy classes of subgroups; only the 923 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 923 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. #13071792 | C2 | direct (N × H) |
| 3. C2×#10622278 | C2 | semidirect |
| 4. C2×#10622550 | C2 | semidirect |
| 5. C2×C11×#383 | C2 | semidirect |
| 10. C2×#66927 | C4 | semidirect |
| 12. C11×#383 | C22 | semidirect |
| 15. #10622550 | C22 | semidirect |
| 16. #10622278 | C22 | semidirect |
| 23. C22×D44 | C2×C4 | semidirect |
| 27. C2×C42×C11 | C2×C4 | semidirect |
| 31. #66927 | C2×C4 | semidirect |
| 50. C2×D44 | C22×C4 | semidirect |
| 53. C42×C11 | C22×C4 | semidirect |
| 59. C2×#383 | D11 | semidirect |
| 86. #383 | C2×D11 | semidirect |
| 113. C2×C42 | C4×D11 | semidirect |
| 117. C2×C11 | #2380 | semidirect |
| 140. C42 | C2×C4×D11 | semidirect |
| 141. C11 | C2×#2380 | semidirect |
| 172. C2 | #13071792 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66927 | 2 |
| #13071792 | 2 |
| C2×#10622278 | 2 |
| C2×#10622550 | 2 |
| C2×C11×#383 | 2 |
| C2×#2380 | 11 |