Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #13071726 | C2 | semidirect |
| 3. #13067239 | C2 | semidirect |
| 4. #13067124 | C2 | semidirect |
| 5. #13066509 | C2 | semidirect |
| 6. #13066508 | C2 | semidirect |
| 7. C11×#1505 | C2 | semidirect |
| 14. #10622699 | C4 | semidirect |
| 15. #10622687 | C4 | semidirect |
| 35. C11×C4⋊Q8 | C2×C4 | semidirect |
| 36. C11×#127 | C2×C4 | semidirect |
| 79. #66867 | C2×C4 | semidirect |
| 144. #1505 | D11 | semidirect |
| 263. C4⋊Q8 | C4×D11 | semidirect |
| 264. #127 | C4×D11 | semidirect |
| 365. C11 | #9441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079084 | 2 |
| #13071726 | 2 |
| #13067239 | 2 |
| #13067124 | 2 |
| #13066509 | 2 |
| #13066508 | 2 |
| C11×#1505 | 2 |
| #9441 | 11 |