Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
806 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 195 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. C22×C16×D11 | C2 | semidirect |
| 3. C2×#10622496 | C2 | semidirect |
| 4. #13070703 | C2 | direct (N × H) |
| 5. C2×#10622129 | C2 | semidirect |
| 6. C2×C11×#366 | C2 | semidirect |
| 15. C2×D176 | C22 | semidirect |
| 17. C2×C16×D11 | C22 | semidirect |
| 19. #10622496 | C22 | semidirect |
| 20. C11×#366 | C22 | semidirect |
| 21. #10622129 | C22 | semidirect |
| 39. C2×C11×C16 | D4 | semidirect |
| 79. C11×C16 | C2×D4 | semidirect |
| 85. C2×#366 | D11 | semidirect |
| 94. C22×D11 | D16 | semidirect |
| 128. #366 | C2×D11 | semidirect |
| 141. C2×D11 | C2×D16 | semidirect |
| 168. C2×C16 | D44 | semidirect |
| 173. C2×C11 | #2215 | semidirect |
| 210. C16 | C2×D44 | semidirect |
| 211. C11 | C2×#2215 | semidirect |
| 259. C2 | #13070703 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D176 | 2 |
| C22×C16×D11 | 2 |
| C2×#10622496 | 2 |
| #13070703 | 2 |
| C2×#10622129 | 2 |
| C2×C11×#366 | 2 |
| C2×#2215 | 11 |