Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
610 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 203 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. #13070850 | C2 | direct (N × H) |
| 3. C2×#10622130 | C2 | semidirect |
| 5. C2×C4×C11⋊C16 | C2 | semidirect |
| 6. C2×C11×#499 | C2 | semidirect |
| 13. C11×#499 | C22 | semidirect |
| 20. #10622130 | C22 | semidirect |
| 22. C4×C11⋊C16 | C22 | semidirect |
| 81. C2×#499 | D11 | semidirect |
| 117. #499 | C2×D11 | semidirect |
| 165. C2×C11 | #2242 | semidirect |
| 199. C11 | C2×#2242 | semidirect |
| 236. C2 | #13070850 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622309 | 2 |
| #13070850 | 2 |
| C2×#10622130 | 2 |
| C2×#10622129 | 2 |
| C2×C4×C11⋊C16 | 2 |
| C2×C11×#499 | 2 |
| C2×#2242 | 11 |