Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 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. #13079275 | C2 | semidirect |
| 3. #13070836 | C2 | semidirect |
| 4. #13070793 | C2 | semidirect |
| 5. #13070698 | C2 | semidirect |
| 7. #13070509 | C2 | semidirect |
| 8. C11×#2166 | C2 | semidirect |
| 20. #10622329 | C22 | semidirect |
| 24. #10622312 | C22 | semidirect |
| 26. #10622296 | C22 | semidirect |
| 27. C11×#364 | C22 | semidirect |
| 29. C11×#347 | C22 | semidirect |
| 31. #10622155 | C22 | semidirect |
| 32. #10622151 | C22 | semidirect |
| 124. #2166 | D11 | semidirect |
| 171. #364 | C2×D11 | semidirect |
| 175. #347 | C2×D11 | semidirect |
| 276. C11 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079275 | 2 |
| #13077520 | 2 |
| #13070836 | 2 |
| #13070793 | 2 |
| #13070698 | 2 |
| #13070569 | 2 |
| #13070509 | 2 |
| C11×#2166 | 2 |
| #33693 | 11 |