Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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. #13068641 | C2 | semidirect |
| 4. #13066523 | C2 | semidirect |
| 5. C11×#1810 | C2 | semidirect |
| 8. C2×#66954 | C4 | semidirect |
| 15. #10622723 | C4 | semidirect |
| 19. #10622715 | C4 | semidirect |
| 20. #10622714 | C4 | semidirect |
| 116. #1810 | D11 | semidirect |
| 298. C11 | #8629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077310 | 2 |
| #13068641 | 2 |
| #13067160 | 2 |
| #13066523 | 2 |
| C11×#1810 | 2 |
| #8629 | 11 |