Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
334 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 67 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. C22×D176 | C2 | semidirect |
| 2. C2×#10622157 | C2 | semidirect |
| 3. #13066793 | C2 | semidirect |
| 4. C22⋊(C11⋊C32) | C2 | semidirect |
| 5. C11×#2215 | C2 | semidirect |
| 7. C2×C11×D16 | C22 | semidirect |
| 13. C11×#366 | C22 | semidirect |
| 16. C2×C11⋊C32 | C22 | semidirect |
| 33. D176 | D4 | semidirect |
| 59. #2215 | D11 | semidirect |
| 86. C2×D16 | C2×D11 | semidirect |
| 91. #366 | C2×D11 | semidirect |
| 98. C22×C11 | D32 | semidirect |
| 153. C11 | #13661 | semidirect |
| 183. C22 | #10622157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D176 | 2 |
| C2×#10622157 | 2 |
| #13066793 | 2 |
| C22⋊(C11⋊C32) | 2 |
| C11×#2215 | 2 |
| #13661 | 11 |