Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2122 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13077282 | C2 | semidirect |
| 2. #13077254 | C2 | semidirect |
| 3. #13077249 | C2 | semidirect |
| 4. C2×#10622537 | C2 | semidirect |
| 6. #13077035 | C2 | semidirect |
| 22. #10622613 | C22 | semidirect |
| 23. #10622610 | C22 | semidirect |
| 24. #10622539 | C22 | semidirect |
| 25. #10622538 | C22 | semidirect |
| 28. #10622537 | C22 | semidirect |
| 29. C2×C4⋊(C11⋊C8) | C22 | semidirect |
| 302. C11 | #60125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077282 | 2 |
| #13077254 | 2 |
| #13077249 | 2 |
| C2×#10622537 | 2 |
| #13077061 | 2 |
| #13077035 | 2 |
| C2×C4×C11×#41 | 2 |
| #60125 | 11 |