Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
536 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 131 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. #13079266 | C2 | semidirect |
| 2. #13077520 | C2 | semidirect |
| 3. #13070831 | C2 | semidirect |
| 4. #13070793 | C2 | semidirect |
| 5. #13070693 | C2 | semidirect |
| 6. #13070564 | C2 | semidirect |
| 7. #13070516 | C2 | semidirect |
| 8. C11×#2166 | C2 | semidirect |
| 21. #10622324 | C22 | semidirect |
| 24. #10622308 | C22 | semidirect |
| 26. #10622296 | C22 | semidirect |
| 27. C11×#364 | C22 | semidirect |
| 29. C11×#347 | C22 | semidirect |
| 31. #10622154 | C22 | semidirect |
| 32. #10622151 | C22 | semidirect |
| 124. #2166 | D11 | semidirect |
| 174. #364 | C2×D11 | semidirect |
| 178. #347 | C2×D11 | semidirect |
| 282. C11 | #33692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079266 | 2 |
| #13077520 | 2 |
| #13070831 | 2 |
| #13070793 | 2 |
| #13070693 | 2 |
| #13070564 | 2 |
| #13070516 | 2 |
| C11×#2166 | 2 |
| #33692 | 11 |