Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
688 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 151 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. C2×#10622728 | C2 | semidirect |
| 2. #13070802 | C2 | semidirect |
| 3. #13070719 | C2 | semidirect |
| 4. #13070530 | C2 | semidirect |
| 5. C11×#2112 | C2 | semidirect |
| 8. C22×D88 | C22 | semidirect |
| 9. C2×C11×M32 | C22 | semidirect |
| 13. #10622728 | C22 | semidirect |
| 15. C2×#66882 | C22 | semidirect |
| 16. C2×D176 | C22 | semidirect |
| 17. C11×C22⋊C16 | C22 | semidirect |
| 18. #10622147 | C22 | semidirect |
| 19. #10622143 | C22 | semidirect |
| 79. #2112 | D11 | semidirect |
| 111. C2×M32 | C2×D11 | semidirect |
| 120. C22⋊C16 | C2×D11 | semidirect |
| 196. C11 | #33758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622728 | 2 |
| #13070802 | 2 |
| #13070719 | 2 |
| #13070530 | 2 |
| C11×#2112 | 2 |
| #33758 | 11 |